Introduction to Matrix Analysis

In this note we introduce the basic concepts of matrix analysis. We begin with a brief review of basic concepts in linear algebra, and then discuss analytical properties of matrices, including matrix norms, matrix decompositions, and matrix functions.

Linear Algebra Review

Given a matrix $A \in \mathbb{C}^{m \times n}$,

Matrix Norms

Matrix Decompositions

Matrix Functions

Real Matrix Analysis

Non-negative Matrices