Algebraic Multiplicity

The algebraic multiplicity of an eigenvalue is the multiplicity of that scalar as a root of the characteristic polynomial of a linear operator or matrix; it counts how many times the eigenvalue appears as a factor (λ − λ0) in the characteristic polynomial.

The exponent of an eigenvalue as a root of the characteristic polynomial of a linear operator or matrix; equivalently, the power of the corresponding linear factor in the polynomial factorization.