Matrix Theory And Linear Algebra
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 the most important theorems are provided.
Contents
1 System 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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