Introduction to Linear Algebra, Fifth Edition (2016)

Publication May 2016

Gilbert Strang linearalgebrabook@gmail.com

Wellesley-Cambridge Press and SIAM (for ordering information)
Book Order Form

Introduction to Linear Algebra, Indian edition, will be published by Wellesley Publishers

Review of the 5th edition by Professor Farenick for the International Linear Algebra Society

ISBN: 978-09802327-7-6

[Table of Contents]

Practice Exam Questions

I hope this website will become a valuable resource for everyone learning and doing linear algebra. Here are key links:

Table of Contents
Preface
Section 1.3 of the book: Matrices
Section 2.5 of the book: Inverse Matrices
Section 3.5 of the book: Dimensions of the Four Subspaces
Section 6.1 of the book: Introduction to Eigenvalues
Section 7.1 of the book: Image Processing by Linear Algebra
Section 12.1 of the book: Mean, Variance, and Probability
Matrix Factorizations
Index
6 Great Theorems
18.06 OpenCourseWare site with video lectures 18.06 on OCW
The publisher's site for the textbook www.wellesleycambridge.com
Solution Manual for the Textbook (updated August 2017)
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8
- Chapter 9
- Chapter 10
- Chapter 11
- Chapter 12
Book Order Form

** 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 (write to linearalgebrabook@gmail.com)

Table of Contents for Introduction to Linear Algebra (5th edition 2016)

1 Introduction to Vectors
- 1.1 Vectors and Linear Combinations
- 1.2 Lengths and Dot Products
- 1.3 Matrices
2 Solving Linear Equations
- 2.1 Vectors and Linear Equations
- 2.2 The Idea of Elimination
- 2.3 Elimination Using Matrices
- 2.4 Rules for Matrix Operations
- 2.5 Inverse Matrices
- 2.6 Elimination = Factorization: A = LU
- 2.7 Transposes and Permutations
3 Vector Spaces and Subspaces
- 3.1 Spaces of Vectors
- 3.2 The Nullspace of A: Solving Ax = 0 and Rx = 0
- 3.3 The Complete Solution to Ax = b
- 3.4 Independence, Basis and Dimension
- 3.5 Dimensions of the Four Subspaces
4 Orthogonality
- 4.1 Orthogonality of the Four Subspaces
- 4.2 Projections
- 4.3 Least Squares Approximations
- 4.4 Orthonormal Bases and Gram-Schmidt
5 Determinants
- 5.1 The Properties of Determinants
- 5.2 Permutations and Cofactors
- 5.3 Cramer’s Rule, Inverses, and Volumes
6 Eigenvalues and Eigenvectors
- 6.1 Introduction to Eigenvalues
- 6.2 Diagonalizing a Matrix
- 6.3 Systems of Differential Equations
- 6.4 Symmetric Matrices
- 6.5 Positive Definite Matrices
7 The Singular Value Decomposition (SVD)
- 7.1 Image Processing by Linear Algebra
- 7.2 Bases and Matrices in the SVD
- 7.3 Principal Component Analysis (PCA by the SVD)
- 7.4 The Geometry of the SVD
8 Linear Transformations
- 8.1 The Idea of a Linear Transformation
- 8.2 The Matrix of a Linear Transformation
- 8.3 The Search for a Good Basis
9 Complex Vectors and Matrices
- 9.1 Complex Numbers
- 9.2 Hermitian and Unitary Matrices
- 9.3 The Fast Fourier Transform
10 Applications
- 10.1 Graphs and Networks
- 10.2 Matrices in Engineering
- 10.3 Markov Matrices, Population, and Economics
- 10.4 Linear Programming
- 10.5 Fourier Series: Linear Algebra for Functions
- 10.6 Computer Graphics
- 10.7 Linear Algebra for Cryptography
11 Numerical Linear Algebra
- 11.1 Gaussian Elimination in Practice
- 11.2 Norms and Condition Numbers
- 11.3 Iterative Methods and Preconditioners
12 Linear Algebra in Probability & Statistics
- 12.1 Mean, Variance, and Probability
- 12.2 Covariance Matrices and Joint Probabilities
- 12.3 Multivariate Gaussian andWeighted Least Squares
Matrix Factorizations
Index
Six Great Theorems / Linear Algebra in a Nutshell

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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. 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.

The words "motion compensation" refer to a way to estimate each video image from the previous one. The simplest would be to guess that successive video images are the same. Then we would only need the changes between frames -- hopefully small. But if the camera is following the action, the whole scene will shift slightly and need correction. A better idea is to see which way the scene is moving and build that change into the next scene. This is MOTION COMPENSATION. In fact the motion is allowed to be different on different parts of the screen.

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. Engineers do their job. I hope these links give an idea of the detail needed.

Introduction to Linear Algebra, Fifth Edition (2016)

Publication May 2016

Table of Contents for Introduction to Linear Algebra (5th edition 2016)

Introduction to Linear Algebra, International Edition

Practice Exam Questions

Linear Algebra Problems in Lemma

The H.264 Video Standard (promised in Section 7.1 of the book)

Singular Value Decomposition of Real Matrices