Linear Algebra for Everyone

From Gilbert Strang, a new approach to linear algebra that is suitable for everyone, going from basics to the singular value decomposition.

Gilbert Strang (Author)

9781733146630, Wellesley

Hardback, published 26 November 2020

368 pages
24.2 x 19.6 x 2.2 cm, 0.8 kg

'The author certainly makes every effort to explain all the concepts in great detail with well-chosen examples, and he provides a huge number of problems including 'challenge problems' and 'recommended problems'. There are also extensive web resources available.' Peter Giblin, University of Liverpool, The Mathematical Gazette

Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.

Preface
1. Vectors and Matrices
2. Solving Linear Equations Ax = b
3. The Four Fundamental Subspaces
4. Orthogonality
5. Determinants and Linear Transformations
6. Eigenvalues and Eigenvectors
7. The Singular Value Decomposition (SVD)
8. Learning from Data
Appendix 1. The Ranks of AB and A + B
Appendix 2. Eigenvalues and Singular Values: Rank One
Appendix 3. Counting Parameters in the Basic Factorizations
Appendix 4. Codes and Algorithms for Numerical Linear Algebra
Appendix 5. Matrix Factorizations
Appendix 6. The Column-Row Factorization of a Matrix
Appendix 7. The Jordan Form of a Square Matrix
Appendix 8. Tensors
Appendix 9. The Condition Number
Appendix 10. Markov Matrices and Perron-Frobenius
Index
Index of Symbols
Six Great Theorems / Linear Algebra in a Nutshell.

Subject Areas: Pattern recognition [UYQP], Maths for engineers [TBJ], Mathematical modelling [PBWH], Algebra [PBF]