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The characteristic polynomial *p*(λ) of an *n*×*n* matrix **A** is defined by *p*(λ)=det(**A**−λ**I**). 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}(*λ*^{n} + *b*_{n−1}*λ*^{n−1} + ⋯ + *b*_{1}*λ* + *b*_{0}),

then **A**^{n}+*b*_{n−1}**A**^{n−1} +…+ *b*_{1}**A**+*b*_{0}**I**=**O**.

*Subjects:*
Mathematics.

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