# Characteristic polynomial

### Functions with Odd Powers

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### For the minimal polynomial of an algebraic element of a field, see Minimal polynomial (field theory). In linear algebra, the minimal polynomial Î¼A of an n Ã— n matrix A over a field F is the monic polynomial P over F of least degree such that P(A) = 0. Any other polynomial Q with Q(A) = 0 is a (polynomial) multiple of Î¼A. The following three statements are equivalent: Î» is a root of Î¼A, Î» is a root of the characteristic polynomial Ï‡A of A, Î» is an eigenvalue of matrix A. Theâ€¦

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