Definition for "Characteristic Polynomial" in the Quantum Dictionary

Natural & Formal Sciences Dictionary

For a square linear operator or matrix A, the polynomial p_A(λ) = det(A - λI) whose roots are the scalar parameters for which A - λI is singular.

- Pure Mathematics -

Algebra Dictionary

For an n×n matrix A or linear operator, the characteristic polynomial is the monic polynomial p(λ)=det(λI−A) whose roots are the eigenvalues of A (over an algebraic closure), with multiplicities equal to algebraic multiplicities.