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21
So, drawing from:

Linear Control Systems Analysis and Design
Conventional and Modern
Third Edition
John D'Azzo and Constantine Houpis
1988

So, above I talked about the matrix program TOTAL, coming from a thesis by S. J. Larimer, at the Air Force Institute of Technology, Wright-Patterson AFB Ohio, 1978

Now we also have other Air Force Institute of Technology theses listed:

Colgate, A.  "INTERAC -An Interactive Software Package for Direct Digital Control Design 1977

Gembrowski, C. J. "Continued Development of an Interactive Computer-Aided Design (CAD) Package for Discrete and Continuous Control System Analysis and Synthesis, 1982

Hernandez, G. "An Interactive Computational Aerodynamics Analysis Program, 1980

Kennedy, A. "The Design of Digital Controllers for the C-141 Aircraft Using Entire Eigenstructure Assignment and the Development of an Inter-Active Computure Design Program, 1979

Logan, G. T.  "Development of an Interactive Computer-Aided Design Program for Digital and Continuous Control System Analysis and Synthesis", 1982

O'Brien, L. "A Consolidated Computer Program for Control System Design", 1976

And I am sure that MatLAB arose from this work.

22
Design and Simulation Software for Controls, Filtering, Signal Processing

Linear control system analysis and design : conventional and modern / John J. D'Azzo, Constantine H. Houpis (1988) 3rd edition. The earlier editions were 1960 and 1981.

This book has an appendix about an Air Force FORTRAN TOTAL, or TOTAL-I.

This is also covered in the 1981 2nd edition.

These D'Azzo and Houpis editions are the only place I have seen TOTAL mentioned.

From when I first learned of MATLAB, I felt that this TOTAL was one of the influences behind it.

TOTAL comes from an MS Thesis

Larimer, S. J. "An Interactive Computer-Aided Design Program for Digital and Continuous System Analysis and Synthesis (TOTAL), School of Engineering, Air Force institute of Technology, Wright-Patterson AFB, Ohio, 1978
23
Industrial Concerns / Re: D'Azzo and Houpis, 1960
« Last post by forbitals on February 10, 2022, 06:49:19 pm »
Linear control system analysis and design : conventional and modern / John J. D'Azzo, Constantine H. Houpis (1988)

So this is newer than the last edition I had ever seen.  But it is similar.  A very big book.

It has all the old stuff going back to 1960.

But it also has stuff about Time Domain Modern Controls.  I would still say that this is only scratching the surface.  No adaptive controls, and no H-Infinity controls or anything like that, and certainly no fuzzy or neural network controls.  THough I suspect that some don't see that as stuff to be taken seriously.  I would like to read the differing views though.

Last chapter is on z-transform, as opposed to Laplace transform, for digital.  But I would still say that this is just scratching the surface.

And of course I will be wanting to record lots of references.



Miles Davis
https://www.youtube.com/watch?v=-8TdZFVj6tA&list=PLl5SPaJlHhZcfhfBMMd8gduvSu_soAd4h&index=3
24
Philosophy, Religion, Esoteric, Occult / April D. DeConick
« Last post by forbitals on February 04, 2022, 04:49:37 pm »
The Gnostic New Age
by April E. DeConick


To clarify, 2nd century Gnostic rites fall into four categories


1.  ceremonies to awaken or quicken the spirit from unconsciousness\
2.  ceremonies to purge the soul of its demons
3.  ceremonies to mature the fledgling spirt into an adult divinity
4.  ceremonies to integrate the mature spirit, the reals self, with its transcendent root.  This process brings healing because it repairs the separation that was the root cause of the person's anxiety and fear, without completely wiping out the individual's identity.


She deals with Darren Aronofsky, director of Requiem for a Dream, which has been talked about on this board.  But she deals with another of his films

Darren Aronofsky

Pi (1998)
https://www.imdb.com/title/tt0138704/?ref_=nm_knf_i1

She deals with John's Gospel, a Gnostic reading.  And she looks at Chapter 4, the Samaritan Woman at the well.  Gnosticism did focus on recruiting Samaritans, and Simon Magus was a big part of this.  As Tobias Churton writes, "He was the original Jesus."

Now lets look at more of DeConick's references:

Clinard, Marshall B., and Robert F. Meier, 2008, Sociology of Deviant Behavior, 13th ed

Couliano, Ioan P. 1992  The Tree of Gnosis: Gnostic Mythology from Early Christianity to Modern Nihilism

Bloom 1992
The American Religion

1996
Omens of Millennium: The Gnosis of Angels, Dreams, and Resurrection

Smoley 2006
Forbidden Faith: The Secret History of Gnosticism

Burfeind, Peter M. 2014
Gnostic America

Wilson Eric G. 2006
Secret Cinema: Gnostic Vision in Film

Fuller, Robert C. 2001
Spiritual, but Not Religious: Understanding Unchurched America

Sheldrake, Philip 2007
A Brief History of Spirituality

Kaufman, Gordon D. 1993
In Face of Mystery: Constructive Theology

Mastrocinque, Attilio, From Jewish Magic to Gnosticism (2005)

Markschies, Christopher, Gnosis: An Introduction (2003)

A lot of talk about Plato, and about The Truman Show.

She is saying that Gnosticism started in Egypt.

Broek, Roelof van den, Gnostic Religion in Antiquity, (2013)

Atum was the hermaphrodite who created himself.

The first Ogdoad was

Shu and Tefnut (manifestation of Maat)
Get and Nut
Osiris, Isis, Nephthys, and Seth

And this is going by both the Coffin Texts and the Pyramid Texts.

Framkfurter, David. 1994
The Magic of Writing and the Writing of Magic: The Power of the Word in Egyptian and Greek Traditions

1998
Religion in Roman Egypt: Assimilation and Resistance

She really emphasizes The Truman Show.

And what Gnosticism is really about is the realization that the God Almighty that people profess allegiance to and that keeps the pews and collection plates full is an idol. And so people come to see themselves as higher than this God.

pg 54

"
The Gnostics believed that they had gnosis because they had found and met the hidden God directly, by undertaking an ecstatic quest. What was chocking was that the God they found was not numbered among the gods of the Babylonian, Egyptian, Jewish, or Greek myths that were being worshipped in the temples down the street.
"

 
Two interesting books, both written about the same time, and both starting with Ezekiel's Vision of the Chariot. These books span the gap between religious and occult kabbalah, and the later does not use the Tree of Life diagram.

Kabbalah (1998)
Three Thousand Years of Mystic Tradition
Hanson, Kenneth, 1953-

The Essential Kabbalah (1994)
the Heart of Jewish Mysticism
Daniel C. Matt


more of DeConick's references:

Garth Fowden (1986) The Egyptian Hermes: A Historical Approach tot he Late Pagan Mind

This Simon Magus was really quite a character.

There had been Dositheus, a successor to John the Baptist, and he had this woman Luna. He was challenged by Simon of Gitta (later known as Simon Magus) and he took over the operation and over Luna, who's real name was Helena.

DeConick sees the good in Paul and she shows why a lot of Gnostics like him. But she also shows how he doubled back on himself and on his Damascus Vision.

She works a lot with these movies with religious themes which promote gnosticism.

She shows how John's Gospel was liked by both Catholics and Gnostics, and it does seem to be in part drawn from Gnostic sources.

From other sources, it is believed that John's Gospel was promulgated to replace the Thomas Gospel.


The Gnostic New Age (2016)
April D. DeConick

She is dealing with religiously themed SciFi, like:

The Truman Show

And then talking about Paul though this, and showing why gnostics like much of what he wrote:

Dogma (1999)
www.imdb.com

Seems to be a very dark themed film, and she uses this to show the gnostic interpretation of John's Gospel, and the original author's intent remains unclear. But John is very moving, and this is why:

Dark City (1998)
www.imdb.com

And then she gets into initiatic experiences with:

Altered States (1980) dir Ken Russell
www.imdb.com

She talks about one Cerinthus, a gnostic interpreter of John.

Michael Allen Williams (1996) Rethinking "Gnosticism": An Argument for Dismantling a Dubious Category.


Each of these gnostic groups has its own story of cosmology, creation, fall, and reintegration. They just don't always call them by these names. They always have some explanation for why life might seem off balance. Or to use the Sanskrit term, samsara, the wagon wheel squeaks on its axle.

p176

Second-century Gnostic rites fall into four categories: ceremonies to awaken or quicken the spirit from unconsciousness; ceremonies to mature the fledgling spirit into an adult divinity; and ceremonies to integrate the mature spirit, the real self, with its transcendent root. The process brings healing because it repairs the separation that was the root cause of the person's anxiety and fear, without completely wiping out the individual's identity.

So the Gnostics were not Buddhists. The spirit does not experience emptiness, nor is it reabsorbed into its root so that it no longer exists individually. The Gnostic rites ensure that the personal spirit has grown its own identity, which then unites with its source.

Henry More in 17th Century first coined term Gnosticism


https://en.wikipedia.org/wiki/Joni_Mitchell

The 40 Best Joni Mitchell Songs: A Beginner's Guide
https://www.youtube.com/watch?v=BsWVRN8DDjs&list=PLkPIAonut3gCtrRYG3hFQbzrRT0TB2ApW

Steely Dan - Can't Buy a Thrill (1972) - full album
https://www.youtube.com/watch?v=jmdiKePVUy8&list=PLfGibfZATlGq9jnvz7I1gw5Xp_FYMQ60p&index=1

25
Computers, Math, Science, Technology / Machine Learning, TensorFlow
« Last post by forbitals on February 02, 2022, 04:43:57 pm »
Hands-On Machine Learning with Scikit-Learn and TensorFlow

by Aurelien Geron

O'Reilly (2017)



OSM Martinism
https://www.youtube.com/watch?v=A0octoNHd0w
26
Philosophy, Religion, Esoteric, Occult / Gifted
« Last post by forbitals on January 28, 2022, 04:36:23 pm »
The Gifted Movement is the counter part to the Autism/Aspergers/Neurodiversity Eugenics Hoax.  It is the more reasonable approach.  When one reads the autism narratives their is always a common feature, two extremely intelligent parents who do not recognize and honor their own intelligence.  Instead they see their child as a problem and an embarrassment.  Eventually the child internalizes this, so even if the parents aren't driving them to the doctor, the child will be driving themselves.

The counter view is found in the Gifted Movement.  Though I'm sure I don't agree with all of it, the central ideas I do agree with, and I am working to learn more about it.  It is simply the way it goes when people decide to honor their own intelligence and that of their child.  It what happens when parents stand with their child, where as in the Autism/Aspergers/Neurodiversity families, the parents are exploiting their child.

The Gifted Movement predates the rise in NeoLiberalism in the 1990's which resurrected the Nazi Eugenics concept of Autism/Aspergers.  The Gifted Movement and the Post-Human / Trans-Human movements are the reasonable alternatives.

Genius Denied, by Jan and Bob Davidson(2004)
These are the people who are running a special school which uses part of the U Nevada Reno campus.  They require proof of an IQ of 145.  If you believe in IQ and that it measures anything meaningful, and that the scale is calibrated correctly, than that would be the top 0.7% of the population.

FWIW, in the Organization which I am building we will not be using IQ tests or any other kinds of tests.  But I want to read the above text and understand it.

Here I want to list some other references which I plan to avail myself of:

Real Boys: Rescuing your son from the myths of boyhood (1998)

Colangelo, N.,  Assouline, S. B. (2004),  A nation deceived: How Schools hold back America's Brightest students, 2 volumes

R. Orstien (1991) The evolution of consciousness
The Origins of the way we think

John Vasconcelles, 1990, Toward a state of esteem.

Edelman, Gerald (2004) Wider than the sky: The Phenomenal Gift of Consciousness

Briggs, D. (1970)  Your Child's Self-Esteem: The Key to His Life.

John Curtis Gowan ( taught at what would become CSU Northridge) 
The education and guidance of the ablest / by John Curtis Gowan [and] George D. Demos. With a pref., by Charles Bish, and a foreword by E. Paul Torrance (1964, 511 pages)

The disadvantaged and potential dropout: compensatory educational programs : a book of readings / compiled and edited by John Curtis Gowan and George D. Demos (1966 624 pages)

Educating the ablest : a book of readings on the education of gifted children / edited by John Curtis Gowan and E. Paul Torrance. (1971 295 pages)

Operations of increasing order and other essays on exotic factors of intellect, unusual powers and abilities, etc. (as found in psychic science) ... / John Curtis Gowan (1980 384 pages)

The academically talented student and guidance / [by] John C. Gowan [and] Catherine B. Bruch. (1971 107 pages)

Tyre, P.  (2004) The Trouble With Boys

Strang, R.  The Psychology of Gifted Children (1965), Helping Your Gifted Child (1961)

Hollingsworth, L. S.

Klein, A. (2002) A forgotten voice: A biography of Leta Stetter Hollingworth

K. Dabrowski, Positive Disintegration and Pschoneurosis is not an illness (1972), Kazimierz Dabrowski (1902-1980)

Nelson, K. C. and Piechowski M. M. wrote about Dabrowski

Spiegel, J. P. the resolution of role conflict within the family, 1957 article.

Levy, D. M. Maternal Overprotection (1943)

Henri Bergson, Creative Evolution (1944)
 
R. M., Bucke, Cosmic Consiousness, 6th ed 1929

Louis Bulk??  1926, The Causes of Evolution, Foetalization of the Ape

Dabrowski, K. and Piechowski, M. M.  Theory of levels of Emotional Development, 2 volumes, 1977
27
Industrial Concerns / General Motors Pickup Trucks
« Last post by forbitals on January 24, 2022, 04:27:37 pm »
General Motors Full-Size Trucks 1980-87 Repair Manual
Gasoline and Diesel
Chilton's, An American Tradition Since 1925

The smog control gear on the vehicles of this era are extremely complicated.  I think it got easier when they went to sequential fuel injection and everything behing handled through the computer.  But to understand where it all came from, the extreme complexity, is why I picked up the book.  So let me go straight to the emission controls section.

Positive Crankcase Ventilation
to evacuate the crankcase of vapors
PCV valve meters the air flow rate, to maintain idle quality.  Valve sits in grommet in top of left valve cover.

Crankcase breather hose goes from right side valve cover to air filter housing.  Has its own little filter.  In some "abnormal" situations it would send crankcase vapors back up and into the intake.

Air Injector Reactor (A.I.R.)
the smog pump.  Injects air near the exhaust valve.  Has diverter valve, check valve, and its own filter

Pulse Air Injection (PAIR)
exhaust gas pulses siphon fresh air into the exhausts. Has check valves.  Mostly on I6 engines.

Thermostatic Air Cleaner (Thermac) on all gasoline engines.  Uses damper controlled by vacuum motor.  Preheats cold inlet air.

Evaporative Emission Control System  (EECS)  about 3 vacuum control valves.  Must use special EVAP rubber tubing.

Early Fuel Evaporation (EFE) valve on flange of exhaust manifold.  For heat rising.  Uses Thermal Vacuum Switch (TVS) which has 3 vacuum control lines

Throttle Return Control (TRC) tries to interdict supper rich mixture you get when you quickly take your foot of the gas and let the throttle close.  This slows it down.

Oxygen Sensor, must never be expose to silicone, can't use silicone sealants on exhaust or intake manifolds.  Do not touch sensor.  If it looks white, it is trashed.  Do not modify pig tail connector, do not solder other stuff to it.  Might have to have exhaust manifold heated to 120 deg F to unscrew.  Don't use regular anti-sieze, because that insulates it.  Use special GM anti-seize for O2 sensors.

Catalytic Converter, gets super hot.  Install with suitable sealants.  (ceramic?)

Trapped Vacuum Spark, prevents drop in vacuum to distributor advance when cold.  Uses Thermal Vaccum Switch (TVS)

Exhaust Gas Recirculation (EGR), feeds back a small amount of exhaust gas.  Seems to have special mid throat port on carburetor.  Purpose is to diffuse peak ignition temperature to prevent oxides of nitrogen from being formed.  Sometimes use ECM (Electronic Control Module)

Electronic Spark Timing (EST) System (California or fuel injected only)

Explains diagnostic codes

Goes into diesel engine

Diesel has vacuum pump

Huge set of vacuum diagrams

Uses Rochester Carburetors

Might have to install grease gun nipples.  Use special grease for power assisted steering, not the same as chassis ball joints.  Don't over fill ball joints so they screw up rubber booties.

For manual transmission and rear axle use 80w 90 GL5.  For automatic use Dextron.  For power steering use special GM fluid or Dextron II.

Has two tie rod adjustments.  But you can get steering wheel of with puller.  Can adjust camber (roofer's square on smooth flat concrete floor best )  Can adjust castor

Shows two Delco Alternators with internal voltage regulators.  These are better than the old two wire externals.  On Chrysler the Drain Charge Ammeter was iconic.  But because of better voltage regulation, and it gets even better, those ammeters are hard to buy now.  Volt meter is sufficient.

One of the Delcos is 3 phase delta, and the other is 3 phase Y.  One has in addition a module of 3 exciter diodes.  The other does not.  There is always a wire for the dashboard warning light.  On the one with the exciter diodes it back feeds to keep the light off.  The other has some internal box to which a schematic is not supplied.

Open front wheel bearings you need to grease.
They say to replace inboard side grease seal every time.

They show cross torque lug nut patterns for 5, 6, and 8 studs.

SJG

Stanley Clarke
https://www.youtube.com/watch?v=UeXWxroVXZE

https://www.youtube.com/watch?v=BW7a1rTIfAA

Buddy Guy, Knock on Wood
https://www.youtube.com/watch?v=5YUbZo6i1VI

https://www.youtube.com/watch?v=hpa6nvfxmLI

Norah Jones, Something
https://www.youtube.com/watch?v=KC42CJoBIwM&list=RDKC42CJoBIwM&start_radio=1

While My Guitar Gently Weeps
https://www.youtube.com/watch?v=CrTMc2i6Lzc&list=RDKC42CJoBIwM&index=7

https://www.youtube.com/watch?v=Xl-BNTeJXjw

THE ROLLING STONES - Hand Of Fate (1976) w/ Billy Preston in Paris
https://www.youtube.com/watch?v=tdkDQ_VSr08

Jumpin' Jack Flash, Paris 1976
https://www.youtube.com/watch?v=36DtA8pIQGI

Honky Tonk Woman
https://www.youtube.com/watch?v=msVM8BqgEDw&list=PLX1HYvnkNjOSktR55syBGU7KdrBt4n9LQ

Only Rock 'n' Roll
https://www.youtube.com/watch?v=Blf_JvS-SzM&list=PLX1HYvnkNjOSktR55syBGU7KdrBt4n9LQ&index=8

Tumblin' Dice
https://www.youtube.com/watch?v=eQ8vBqXWyTY&list=PLX1HYvnkNjOSktR55syBGU7KdrBt4n9LQ&index=12

The Rolling Stones - Tumbling Dice - Oakland 1994 w/ early Lisa Fischer
https://www.youtube.com/watch?v=-5MfBAwm8_M

https://www.youtube.com/watch?v=S7Eb0JDRtgg
28
Industrial Concerns / Re: D'Azzo and Houpis, 1960
« Last post by forbitals on January 11, 2022, 02:08:07 pm »
Now more refs from  D'Azzo and Houpis

Burns, R. A., and R. M. Saunders "Analysis of Feedback Control Systems" McGraw-Hill, 1955
Analysis of feedback control systems; servomechanisms and automatic regulators [by] Robert A. Bruns [and] Robert M. Saunders (1955)

Doherty, R. E., and E. G. Keller "Mathematics of Modern Engineering", Wiley, 1936
Mathematics of modern engineering ... by Robert E. Doherty ... and Ernest G. Keller (1936, 2 volumes)

Weber, E. "Linear Transient Analysis" Wiley, 1954
0

Electrical Engineering Staff, Massachusetts Institute of Technology, "Electric Circuits" MIT Press, 1940
0

Truxal, J. G. "Automatic Feedback Control Systems Synthesis", McGraw-Hill, 1955
Automatic feedback control system synthesis
*

Gardner, M. F. and J. L. Barnes "Transients in Linear Systems", Wiley, 1942
Transients in linear systems studied by the Laplace transformation [by] Murray F. Gardner ... and John L. Barnes (1942)
*

Churchill, R. V. "Operational Mathematics" McGraw-Hill 1958
    Operational mathematics / [by] Ruel V. Churchill (1971 3rd edition, earlier 1958 edition also available)
*

Thomson, W. T. "Laplace Transformation" Prentice-Hall, 1950
Thomson, William Tyrrell. Laplace transformation : theory and engineering applications. (1950)
*

Guillemin, E. A. "The Mathematics of Circuit Analysis", Wiley, 1949
The mathematics of circuit analysis : extensions to the mathematical training of electrical engineers / Ernst A. Guillemin. (1950)
*

Brown, G. S., and D. P. Campbell, "Principles of Servomechanisms", Wiley, 1948
Principles of servomechanisms; dynamics and synthesis of closed-loop control systems [by] Gordon S. Brown [and] Donald P. Campbell (1948)
0
29
Industrial Concerns / D'Azzo and Houpis, 1960
« Last post by forbitals on January 10, 2022, 06:26:37 pm »
D'Azzo and Houpis, 1960

D'Azzo and Houpis, 1960

The reason I wanted such an old book is real simple.  I wanted to see what it talks about and what it fails to talk about.  I wanted to see what they feel they must explain, and what they feel they can just assume people understand.

This is one of the classic texts and I am familiar with later editions.  They are interesting, but there is also a lot of stuff they do not cover.

Today, if you want to do anything with this, you want to develop computer software.  You want programs to do the computations.  But you also want embedded software to go into your system.  And then you want test bench software to chronicle how your stuff works, and to the the necessary model parameters. 

And you want newer much more sophisticated theory, going further than what this book covers.

And then I also want the old references in this book, especially the math books.  So let me start with these references.

References:

Trinks, W.  "Governors and the Governing of Prime Movers" 1919
Governors and the governing of prime movers / by W. Trinks, 140 illustrations.
+

Bode, H. W. "Network Analysis and Feedback Amplifier Design", 1945
Network analysis and feedback amplifier design, by Hendrik W. Bode (1945)
+

Blackburn, J. F. "Components Handbook" McGraw-Hill, 1948
Components handbook / ed by John F. Blackburn [under the supervision of the Office of Scientific Research and Development, National Defence Research Committee. (1949)
Blackburn, John Francis
+

Wylie, C. R. Jr. "Advanced Engineering Mathematics", McGraw-Hill, 1951
Wylie, Clarence Raymond, 1911-   Advanced engineering mathematics (1951)  first edition, 640 pages.  Later editions of this too, but they have more pages.
+

Corcoran, G. F., and R. M. Kerchner, "Alternating-current Circuits", 3rd edition, John Wiley and Sons, 1951
Alternating-current circuits, by Russell M. Kerchner ... and George F. Corcoran ... (1943, and then also later editions)

Gardner, M. F. and J. L. Barnes "Transients in Linear Systems" John Wiley and Sons, 1942
Transients in linear systems studied by the Laplace transformation [by] Murray F. Gardner ... and John L. Barnes (1942)
*

Trimmer, J. D. "Response of Physical Systems" John Wiley and Sones, 1950
Trimmer, J. D., Response of physical systems., New York, Wiley [1950]
*

"Flow Meters, Their Theory and Application" American Society of Mechanical Engineers, 1937
0
but there is also this: Notes on small flow meters for air : especially orifice meters / by Edgar Buckingham, Physicist, Bureau of Standards. 1921
0


30
Computers, Math, Science, Technology / Re: Linear Algebra and Matrix Math
« Last post by forbitals on December 29, 2021, 01:59:03 pm »
Gilbert Strang, Linear Algebra and Its Applications

more references:
APPLIED LINEAR ALGEBRA

B. Noble, "Applied Linear Algebra" 1969


NUMERICAL LINEAR ALGEBRA

G. Forsythe and C. Moler, "Computer Solution of Linear Algebraic Systems" 1967

C. L. Lawson and R. J. Hanson, "Solving Least Squares Problems" 1974

G. W. Stewart, "Introduction to Matrix Computations", 1973

R. S. Varga, "Matrix Iterative Analysis", 1962

J. M. Wilkinson, "Rounding Errors in Algebraic Processes", 1963

J. M. Wilkinson, "The Algebraic Eigenvalue Problem", 1965

J. M. Wikinson and C. Reinsch, eds, "Handbook for Automatic Computation II, Linear Algebra", Springer, 1971

D. M. Young, "Iterative Solution of Large Linear Systems", 1971




Gilbert Strang
Linear Algebra and Its Applications
1976, 1st edition
Strang was at MIT

Before forget, let me say that Strang does talk some about Regression Analysis, Factor Analysis, and Principle Component Analysis

So he starts out explaining that primarily linear algebra is about simultaneous equations and Gaussian elimination.  The second idea will be determinants and Cramer's rule.

He will show Gaussian Elimination and talk about zero pivots and when you have a singular matrix.  It will get into LU factorization, which results from Gaussian Elimination.  And then you use back substitution.

Tends to be n^2 operations for Gaussian Elimination.

So he talks about Matrix Multiplication.

So you will be doing Gaussian Elimination, and you will be logging the results in an Elementary Matrix, E.

So you will premultiply Ax  with E, on both sides, and matrix multiplication is associative.

So you get this upper triangular matrix, and these various E matrices which log what was done to get it, cause you will want to back substitute for your solution.

Usually you will want to do row substitution in order to get bigger pivots, to avoid zero, but also to minimize round off errors.  I think it is actually biggest ABS pivot.

And so a P matrix to log this is introduced, Permutation Matrix.  You also premultiply both sides by this.

So you are finding the inverse of the original A matrix.  ( the other way of doing this, Determinant and Adujunct Matrices, is extremely slow )

So you use the Gauss-Jordan method:

https://en.wikipedia.org/wiki/Gaussian_elimination

And then he talks about Band Matrices, which are matrices where the only non-zero elements are close to the diagonal.  I guess this is a particular form of the Sparse Matrix

Good links on this:
Sparse Matrix
https://en.wikipedia.org/wiki/Sparse_matrix

Band Matrix
https://en.wikipedia.org/wiki/Band_matrix

He looks at a differential equation with a two point boundary condition.  A geometrical spacer, h, is introduced.  This makes the problem discrete, and how small h is determines the number of equations and the number of unknowns, and of course this results in a band matrix.

So he goes into a more formal theory of simultaneous linear equations, and gets into Vector Spaces and Subspaces, and he goes into graphic representations.

And so we are talking about the row space of A, the nullspace of A, the column space of A, and the left nullspace of A.

Talks about Orthogonality of Vectors and Subspaces.

Fundamental Theorem of Linear Algebra, Part 1 and Part 2.

So, talks about Orthogonal Projections and Least Squares, and starts off talking about Inner Products and Transposes, and the Schwarz Inequality

Projections onto Subspaces and Least Squares

Least Squares solution satisfies "normal equations".

Projection Matrices, P

Least Squares Fitting of Data

Orthogonal Bases, Orthogonal Martices, And Gram-Schmidt Orthogonalization

Hilbert Space
Fourier Series
Legendre Polynomials

Pseudoinverse and the Singular Value Decomposition

Weighted Least Squares

now there is a big change in the book as he shifts to the discussion of Determinants

pg 146:

"The determinant provides and explicit "formula," a concise and definite expression in closed form, for quantities such as A^-1"

gives test for invertibility

gives volume of parallelepiped

Jacobian Determinant
Gilbert Strang, Linear Algebra and Its Applications

more references:
APPLIED LINEAR ALGEBRA

B. Noble, "Applied Linear Algebra" 1969


NUMERICAL LINEAR ALGEBRA

G. Forsythe and C. Moler, "Computer Solution of Linear Algebraic Systems" 1967

C. L. Lawson and R. J. Hanson, "Solving Least Squares Problems" 1974

G. W. Stewart, "Introduction to Matrix Computations", 1973

R. S. Varga, "Matrix Iterative Analysis", 1962

J. M. Wilkinson, "Rounding Errors in Algebraic Processes", 1963

J. M. Wilkinson, "The Algebraic Eigenvalue Problem", 1965

J. M. Wikinson and C. Reinsch, eds, "Handbook for Automatic Computation II, Linear Algebra", Springer, 1971

D. M. Young, "Iterative Solution of Large Linear Systems", 1971




Gilbert Strang
Linear Algebra and Its Applications
1976, 1st edition
Strang was at MIT

Before forget, let me say that Strang does talk some about Regression Analysis, Factor Analysis, and Principle Component Analysis

So he starts out explaining that primarily linear algebra is about simultaneous equations and Gaussian elimination.  The second idea will be determinants and Cramer's rule.

He will show Gaussian Elimination and talk about zero pivots and when you have a singular matrix.  It will get into LU factorization, which results from Gaussian Elimination.  And then you use back substitution.

Tends to be n^2 operations for Gaussian Elimination.

So he talks about Matrix Multiplication.

So you will be doing Gaussian Elimination, and you will be logging the results in an Elementary Matrix, E.

So you will premultiply Ax  with E, on both sides, and matrix multiplication is associative.

So you get this upper triangular matrix, and these various E matrices which log what was done to get it, cause you will want to back substitute for your solution.

Usually you will want to do row substitution in order to get bigger pivots, to avoid zero, but also to minimize round off errors.  I think it is actually biggest ABS pivot.

And so a P matrix to log this is introduced, Permutation Matrix.  You also premultiply both sides by this.

So you are finding the inverse of the original A matrix.  ( the other way of doing this, Determinant and Adujunct Matrices, is extremely slow )

So you use the Gauss-Jordan method:

https://en.wikipedia.org/wiki/Gaussian_elimination

And then he talks about Band Matrices, which are matrices where the only non-zero elements are close to the diagonal.  I guess this is a particular form of the Sparse Matrix

Good links on this:
Sparse Matrix
https://en.wikipedia.org/wiki/Sparse_matrix

Band Matrix
https://en.wikipedia.org/wiki/Band_matrix

He looks at a differential equation with a two point boundary condition.  A geometrical spacer, h, is introduced.  This makes the problem discrete, and how small h is determines the number of equations and the number of unknowns, and of course this results in a band matrix.

So he goes into a more formal theory of simultaneous linear equations, and gets into Vector Spaces and Subspaces, and he goes into graphic representations.

And so we are talking about the row space of A, the nullspace of A, the column space of A, and the left nullspace of A.

Talks about Orthogonality of Vectors and Subspaces.

Fundamental Theorem of Linear Algebra, Part 1 and Part 2.

So, talks about Orthogonal Projections and Least Squares, and starts off talking about Inner Products and Transposes, and the Schwarz Inequality

Projections onto Subspaces and Least Squares

Least Squares solution satisfies "normal equations".

Projection Matrices, P

Least Squares Fitting of Data

Orthogonal Bases, Orthogonal Martices, And Gram-Schmidt Orthogonalization

Hilbert Space
Fourier Series
Legendre Polynomials

Pseudoinverse and the Singular Value Decomposition

Weighted Least Squares

now there is a big change in the book as he shifts to the discussion of Determinants

pg 146:

"The determinant provides and explicit "formula," a concise and definite expression in closed form, for quantities such as A^-1"

gives test for invertibility

gives volume of parallelepiped

Jacobian Determinant

https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant

finding determinants needs n! computations!!!

Cramer's Rule

Expansion in cofactors, and finding inverse from adjugate matrix

Then book makes big shift to Eigenvalues and Eigenvectors
https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant

finding determinants needs n! computations!!!

Cramer's Rule

Expansion in cofactors, and finding inverse from adjugate matrix

Then book makes big shift to Eigenvalues and Eigenvectors
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