# Eigenvectors and eigenvalues

Let be an matrix, and let be the zero vector in  whose entries are all zero's. Then we can define a homogeneous equation  , which is a special case of matrix equation with . The homogeneous equation  has always the trivial solution  , but may have nontrivial solutions  .

EXAMPLE 1. Determine whether the homogeneous system

has a nontrivial solution. Then describe the solution set.

Let be an square matrix, and let be the identity matrix. Let be a scalar. If the homogeneous equation

 (9)

has nontrivial solutions, then the scalar  is called an eigenvalue of .

In Matlab/Octave the function eig(A) returns a vector containing eigenvalues of .

Subsections

Department of Mathematics