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Introduction to Linear Algebra, Fifth Edition

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by Gilbert Strang


2016 / x + 574 pages / Hardcover / 978-0-9802327-7-6 / List Price $95.00 / SIAM Member Price $66.50 / Order Code WC14

This fifth edition replaces:

  • Introduction to Linear Algebra, Fourth Edition (Order Code WC09, ISBN 978-0-9802327-1-4)
  • Introduction to Linear Algebra, Third Edition (Order Code WC06, ISBN 978-0-961408-89-3)

which are no longer available.

Published by Wellesley-Cambridge Press. Distributed by SIAM.

Chapter 1: Introduction to Vectors;
Chapter 2: Solving Linear Equations;
Chapter 3: Vector Spaces and Subspaces;
Chapter 4: Orthogonality;
Chapter 5: Determinants;
Chapter 6: Eigenvalues and Eigenvectors;
Chapter 7: The Singular Value Decomposition (SVD);
Chapter 8: Linear Transformations;
Chapter 9: Complex Vectors and Matrices;
Chapter 10: Applications;
Chapter 11: Numerical Linear Algebra;
Chapter 12: Linear Algebra in Probability & Statistics;
Matrix Factorizations;
Six Great Theorems/Linear Algebra in a Nutshell.

This book is designed to help students understand and solve the four central problems of linear algebra:

Ax = b n by n Chapters 1-2 Linear systems
Ax = b m by n Chapters 3-4 Least squares
Ax = λx n by n Chapters 5-6 Eigenvalues
Av = σu m by n Chapters 7-8 Singular values

The diagram on the front cover shows the four fundamental subspaces for the matrix A. Those subspaces lead to the Fundamental Theorem of Linear Algebra:

  1. The dimensions of the four subspaces
  2. The orthogonality of the two pairs
  3. The best bases for all four subspaces

This is the textbook that accompanies the author's video lectures and the review material on MIT's IOpenCourseWare.

ocw.mit.edu and math.mit.edu/linearalgebra

Many universities and colleges (and now high schools) use this textbook. Chapters 8-12 are for a second course on linear algebra.

About the Author
Gilbert Strang is a Professor of Mathematics at Massachusetts Institute of Technology and an Honorary Fellow of Balliol College, of the University of Oxford. His current research interests include linear algebra, wavelets and filter banks, applied mathematics, and engineering mathematics. He is the author or co-author of eight textbooks. Professor Strang served as SIAM's president from 1999-2000, chaired the US National Committee on Mathematics from 2003–2004, and won the John von Neumann Medal of the U.S. Association of Computational Mechanics in 2005 and the Henrici Prize in 2007. He is a Fellow of the American Academy of Arts and Sciences and a member of the National Academy of Sciences.


ISBN: 9780980232776

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