Overview

Information in science and mathematics is often organized into rows and columns to form rectangular arrays, called matrices (plural of matrix ). Matrices are often tables of numerical data that arise from physical observations, but they also occur in various mathematical contexts.

Howard Anton. Elementary Linear Algebra . Wiley (1973 1st edn, 2000 8th edn).

To be able to read or work on matrix computing, a reader must have completed a course on linear algebra. The inclusion of this Appendix A is to review some selected topics from basic linear algebra for reference purposes.

A.1 Linear Independence

Let v _j ? for j = 1, , r with r ? n. The set of r vectors ? ₁, ? ₂, , ? _r is said to be linearly independent if the only solution of the equation

(A.1)

is k ₁ = k ₂ = k ₃ = = k _r = 0. Otherwise, the set of vectors is said to be linearly dependent.

An interesting fact is that equation (A.1) can be put into matrix vector form

(A.2)

Let the subspace V = span ( ? ₁, ? ₂, , ? _n) and the matrix A = [ ? ₁, ? ₂, , ? _n]. Then y ? V is the same as

(A.3)

A.2 Range and Null Spaces

Given...