Table of contents - Linear algebra

This is a table of contents for my notes on linear algebra.

Matrix algebra

• Matrices - basic definitions
• Matrix addition and the zero matrix
• Matrices - scalar multiplication and trace
• Matrix multiplication and powers of a matrix
• Matrix transposes and symmetric and hermitian matrices
• Skew-symmetric and skew-hermitian matrices
• Left and right inverses of matrices
• Singular and nonsingular matrices
• Partitioned matrices

Simple applications

• Markov chain as a business model
• Population growth
• Oscillations in a triatomic molecule
• Fitting a straight line with least squares

Methods for finding inverses and solving equations

• Solving equations by Gaussian elimination
• Matrix inverses with Gaussian elimination
• Elementary matrices
• LU decomposition without interchanges
• LU decomposition with interchanges
• LU decomposition of singular matrices
• LU decomposition of band matrices
• Crout and Doolittle variants of LU decomposition
• Work measures in solving systems of linear equations

Theory of finding inverses and solving equations

• Gauss-reduced form and rank of matrices