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Cayley-Hamilton Theorem


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The characteristic polynomial p(λ) of an n×n matrix A is defined by p(λ)=det(A−λI). The following result about the characteristic polynomial is called the Cayley-Hamilton Theorem:

Theorem

If the characteristic polynomial p(λ) of an n×n matrix A is written

p(λ)=(−1)n(λn + bn−1λn−1 + ⋯ + b1λ + b0),

then An+bn−1An−1 +…+ b1A+b0I=O.

Subjects: Mathematics.


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