forms a linear subspace of 
of dimension
. 
is called the geometric multiplicity of
.
if and only if 
is singular.
has degree
n and is of the form
Its roots are the eigenvalues of 
. 
is called
the characteristic polynomial of .
are the distinct zeroes
of , then 
can be rewritten as
The integer 
(associated with 
) is called the
algebraic multiplicity of .
holds.
be an arbitrary polynomial and be a matrix of order n with
and 
as one of its eigenvalues and corresponding
eigenvector. Then 
is an eigenvalue of 
with
corresponding eigenvector .