Linear algebra gilbert strang
Hem / Utbildning & Karriär / Linear algebra gilbert strang
These are part of his larger teaching site called LEM.MA and he built the page http://lem.ma/LAProb/especially for this website linked to the 5th edition.
The H.264 Video Standard (promised in Section 7.1 of the book)
This video standard describes a system for encoding and decoding (a "Codec") that engineers have defined for applications like High Definition TV.
It is not expected that you will know the meaning of every word -- your book author does not know either. But if the camera is following the action, the whole scene will shift slightly and need correction. Here are key links:
** Each section in the Table of Contents links to problem sets, solutions,
** other websites, and all material related to the topic of that section.
** Readers are invited to propose possible links.
Table of Contents for Introduction to Linear Algebra (5th edition 2016)
[top]
Each section of the book has a Problem Set.
While playing, click the word 'YouTube'
to watch a larger video in a separate tab
Linear transformations of a house
Eigenvalues don't quite meet
Practice Exam Questions
Links to websites for each semester at MIT: web.mit.edu/18.06 ,
Linear Algebra Problems in Lemma
My friend Pavel Grinfeld at Drexel has sent me a collection of interesting problems -- mostly elementary but each one with a small twist.
In fact the motion is allowed to be different on different parts of the screen. The result is to see (for small matrices) the ideas of column rank and row rank and a valuable factorization \(A = CR\).
Later chapters (the heart of the book) develop five great factorizations of a matrix, and they are connected to the four fundamental subspaces that students can work with.
Chapter 10 (the closing chapter) — not reached in a first course but so valuable in modern applications — describes the key ideas of Deep Learning.
A better idea is to see which way the scene is moving and build that change into the next scene.
Linear Algebra
Do problems:
23 and 28 from section 1.2
4 and 13 from section 1.3
29 and 30 from section 2.1
20 and 32 from section 2.2
22 and 29 from section 2.3
32 and 36 from section 2.4
7 from section 2.5
Do problems:
24 and 40 from section 2.5
13, 18, 25, and 26 from section 2.6
13, 36, and 40 from section 2.7
18, 23, 30, and 32 from section 3.1
Do problems:
18, 24, 36, and 37 from section 3.2
19, 25, 27, and 28 from section 3.3.
The learning function (built from training data) is piecewise linear with matrix weights. The simplest would be to guess that successive video images are the same.
It is ideas like this -- easy to talk about but taking years of effort to perfect -- that make video technology and other technologies possible and successful.
Accessibility
This is MOTION COMPENSATION. Problem 17 is optional but recommended13, 25, 28, 35 (MATLAB recommended) and 36 from section 3.4
Do problems:
2, 20, 37, 41, and 44 from section 3.5
11, 24, 28 (with challenge subpart), 30, and 31 from section 3.6
7, 9, 31 (verify this with MATLAB on a 6 by 12 matrix), 32, and 33 from section 4.1
13, 16, 17, 30, 31, and 34 from section 4.2
13 (MATLAB allowed) and 17 from section 8.2
Do problems:
4, 7, 9, 26 and 29 from section 4.3
10, 18, 35, and 36 from section 4.4
10, 18, 31, and 32 from section 5.1 (the last two will be treated as challenge problems)
Do problems:
16, 32, and 33 from section 5.2
8, 28, 40, and 41 from section 5.3
19 and 29 from section 6.1
6, 16, and 37 from section 6.2
Challenge problem in MATLAB
Do problems:
14, 24, 28, 29, and 30 from section 6.3
7, 10, 23, 28, and 30 from section 6.4
9, 12, and 16 (counts as a challenge problem, MATLAB allowed) from section 8.3
Do problems:
25, 26, 27, 29, 32, 33, 34, and 35 from section 6.5
3, 5, 7, 10, and 11 from section 8.1 (last two count as challenge problems)
Do problems:
12, 14, 20, 22, 23, and 24 from section 6.6.
4, 11, and 17 from section 6.7.
4, 5, 12, and 13 from section 8.5 (last two count as challenge problems)
Linear Algebra Animation Videos
I hope this website will become a valuable resource for everyone learning and doing linear algebra.
The point is to see an important example of a "standard" that is created by an industry after years of development--- so all companies will know what coding system their products must be consistent with. Engineers do their job.
Then we would only need the changes between frames -- hopefully small. I hope these links give an idea of the detail needed.
Notes on Linear Algebra
Proof of Schur's Theorem
Singular Value Decomposition of Real Matrices (Prof. Jugal Verma, IIT Bombay, March 2020)
Our recent textbook Linear Algebra for Everyone starts with the idea of independent columns
This leads to a factorization A = CR where C contains those independent columns from A
The matrix R tells how to combine those columns of C to produce all columns of A
Then Section 3.2 explains how to solve Rx = 0.
The words "motion compensation" refer to a way to estimate each video image from the previous one. His video lectures on MIT OpenCourseWare have been viewed over ten million times, and his textbooks have been widely adopted. This gives the nullspace of A !!
Here is that new section : A = CR and Computing the Nullspace by Elimination
This page has been accessed at least times since January 2009.
Linear Algebra
The sixth edition of Gilbert Strang's best-selling textbook, Introduction to Linear Algebra, continues to combine serious purpose with a gentle touch, providing an accessible and comprehensive guide to the study of linear algebra.
For unseen data, those same weights give an accurate understanding — and every student knows the importance of these ideas.
New to the Sixth Edition:
- Two new chapters on applications of linear algebra to vital modern problems of optimization and learning from data.
- Expanded coverage of linear transformations and eigenvectors.
- Revised treatment of singular value decomposition with a focus on its applications in data analysis and machine learning.
- More examples and exercises, helping students to solidify their understanding of the material.
Those combinations fill the column space of \(A\), and the idea of linear independence is introduced by examples. Two of the chapters — the first and the last — deserve special mention.
Chapter 1 emphasizes that matrix-vector multiplication Ax produces a linear combination of the columns of \(A\).