Matrix Theory and Linear Algebra by Peter Selinger

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PDF PRINTED BOOK
BLACK & WHITE
Paperback, 561 PAGES Edition 2020
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Matrix Theory and Linear Algebra is an introduction to linear algebra for students in the first or second year of university. The book contains enough material for a 2-semester course. Major topics of linear algebra are presented in detail, and many applications are given. Although it is not a proof-oriented book, proofs of most important theorems are provided.

Contents

1 Systems of linear equations
2 Vectors in ℝⁿ
3 Lines and planes in ℝⁿ
4 Matrices
5 Spans, linear independence, and bases in ℝⁿ
6 Linear transformations in ℝⁿ
7 Determinants
8 Eigenvalues, eigenvectors, and diagonalization
9 Vector spaces
10 Linear transformation of vector spaces
11 Inner product spaces
Appendix A Complex numbers

List of applications

  • Balancing chemical reactions
  • Dimensionless variables
  • Resistor networks
  • Cryptography: The Hill cipher
  • Perspective rendering
  • Solving recurrences
  • Solving systems of linear differential equations
  • Error correcting codes
  • Fourier series
  • Simplification of quadratic forms
  • Principal component analysis

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