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algebraic multiplicity

How many times an eigenvalue repeats as a root of the characteristic polynomial.

The algebraic multiplicity of an eigenvalue \lambda is its multiplicity as a root of the characteristic polynomial p(t)=\det(A-tI) — the exponent k in p(t)=(\lambda-t)^kq(t) with q(\lambda)\ne 0. It can exceed the eigenvalue's geometric multiplicity, but never falls short of it.

See also

geometric multiplicity characteristic polynomial defective
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