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Characteristic Polynomial

Characteristic Polynomial

Jun 30, 20251 min read

linear-algebra

Definition

Characteristic Polynomial

The characteristic polynomial of a square matrix A∈Fn×n is the determinant:

χA​(λ)=det(λ⋅In​−A)

Note that the degree of this polynomial is n and the leading coefficient is 1. Thus, eigenvalues are the rots of χA​(λ). Since a polynomial of degree n (over a field F) can have at most n distinct roots, an n×n square matrix has at most n eigenvalues.


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