multiplicity of eigenvalue
Suppose is a finite dimensional vector space over a field ,
and suppose is a linear map.
Suppose also that is an
eigenvalue
of , that is, .
The algebraic multiplicity,
denoted by , of
is the multiplicity of the root to the polynomial
.
The geometric multiplicity of , denoted by
, is the
dimension of , the eigenspace
of .
Title | multiplicity of eigenvalue |
---|---|
Canonical name | MultiplicityOfEigenvalue |
Date of creation | 2013-03-22 15:15:15 |
Last modified on | 2013-03-22 15:15:15 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 5 |
Author | matte (1858) |
Entry type | Definition |
Classification | msc 15A18 |
Defines | geometric multiplicity |
Defines | algebraic multiplicity |