# Maxima by Example, Chapter 5: Matrix Solution Methods

### Ted Woollett

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Chapter 5 shows the use of Maxima matrices for the solution of eigenvalue and eigenvector problems,
and the analytic matrix solution of sets of first order ordinary differential equation initial value problems.

This chapter leans heavily on the approach to matrix use found in the Schaum's Outlines text: Matrix Operations, 2nd ed., by Richard Bronson.

- --mbe5matrix.pdf : Mar. 30, 2016, Maxima 5.36.1, 95 pages
- --mbe5matrix.tex : Mar. 30, 2016, Latex code file
- --mbe5.mac : Maxima matrix functions code: Mar. 30, 2016, Maxima 5.36.1

Chapter 5 Topics

- Introduction and Quick Start with Maxima Matrices
- Generalized Eigenvectors
- Jordan Chains, Canonical Basis
- The Jordan Canonical Form
- The Cayley-Hamilton Theorem
- Functions f(A) of a matrix A
- The Matrix e^(A t), given the matrix A
- Analytic solutions of the matrix equation: du/dt = A u(t) for A = a const. matrix and u(0) a given column vector