Algebraic multiplicity
is the multiplicity of the eigenvalue as a root of the characteristic polynomial ; over an algebraically closed field the algebraic multiplicities of an matrix sum to .
Definition 4.6 (Algebraic Multiplicity)
The algebraic multiplicity of an eigenvalue , or , is its multiplicity as a root of the characteristic polynomial .
By the fundamental theorem of algebra, the sum of the algebraic multiplicities of all eigenvalues of an matrix is .
Related
Stated in
- Definition 4.6 (Algebraic Multiplicity)§4.2 Eigenspaces and Multiplicity