Introduction to Linear Algebra, Sixth Edition (2023)
by Gilbert Strang (gilstrang@gmail.com) ISBN : 978-17331466-7-8
Go to Introduction to Linear Algebra (5th Edition) website
Please click on the desired resource to download it or open up a new link
Table of Contents and Preface to the 6th edition (ILA6)
Front and Back Covers and Copyright Page (ILA6)
Typos in the 6th Edition of Introduction to Linear Algebra
Click here to order the book from Wellesley-Cambridge Press (USA)
Textbooks by Gilbert Strang / Video links and book websites
Linear Algebra for Everyone (2020)
Linear Algebra and Learning from Data (2019)
Differential Equations and Linear Algebra
Computational Science and Engineering
Calculus
Sample sections from the book
Section 1.4 : Matrix Multiplication AB and CR
Section 2.2 : Elimination Matrices and Inverse Matrices
Section 3.5 : Dimensions of the Four Subspaces
Section 6.1 : Introduction to Eigenvalues
Appendix 1 : The ranks of AB and A + B
Selected Solutions to Problem Sets (November 2023)
Important links
Matrix World : The Picture of All Matrices, by Kenji Hiranabe
LU and CR Elimination (SIAM Review 64 (2022) 181-190)
Topics from the Fifth Edition
Fourier Series
Norms and Condition Numbers
IterativeMethods and Preconditioners
Linear Algebra for Cryptography
Linear Programming (Section 10.4 of Introduction to Linear Algebra, 5th edition)
Wellesley-Cambridge Press (USA)
Book Order from Wellesley-Cambridge Press (USA)
Book Order for SIAM members
Book Order from American Mathematical Society
Book Order from Cambridge University Press (outside North America)
Book Order from Wellesley Publishers (India only)
Linear Algebra Animation Videos
In the following videos, click the 'Play' ► iconWhile 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
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. 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.
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. This gives the nullspace of A !!
Here is that new section : A = CR and Computing the Nullspace by Elimination
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