Little Linear Algebra Contents: Linear vector spaces Matrices Special Matrices Matrix & vector Norms

Definition of Matrix A matrix is a collection of numbers arranged into a fixed number of rows and columns. Usually the numbers are real numbers. In general, matrices can contain complex numbers but we won't see those here. Here is an example of a matrix with three rows and three columns: The top row is row 1The leftmost column is column 1. This matrix is a 3x3 matrix because it has three rows and three columns. In describing matrices, the format is: rows X columns Each number that makes up a matrix is called an element of the matrix. The elements in a matrix have specific locations.

Transpose of a matrix For matrix A of the form: With 3 rows and 2 columns the transpose is rotate the matrix to change rows into columns and columns into rows In the form The superscript T denotes transpose, sometimes we use * instead of T

Matrix addition

Matrix multiplication Scalar multiplication

Properties of Multiplication

Special structure Matrices 1- identity matrix 2- Diagonal matrix