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

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

has nontrivial solutions, then the scalar is called an

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

Department of Mathematics