Matrix Theory and Linear Algebra by Peter Selinger
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Description
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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