8.1 Matrix Algebra

8.2 Systems of Linear Equations

8.3 Rank of a Matrix

8.4 Determinants

8.5 Properties of Determinants

8.6 Inverse of a Matrix

8.7 Cramer’s Rule

8.8 Eigenvalue Problem

8.9 Powers of Matrices

8.10 Orthogonal Matrices

8.11 Approximation of Eigenvalues

8.12 Diagonalization

8.13 LU-Factorization

8.14 Cryptography

8.15 Error-Correcting Code

8.16 Method of Least Squares

8.17 Discrete Compartmental Models

Chapter 8 in Review

In mathematics one is often faced with the task of handling large arrays of numbers or functions. Such work is often expedited by using a matrix. The theory of matrices was the invention of the prolific English mathematician Arthur Cayley (1821–1895).