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