Prove, about characteristic polynomial...

GOKILL · **Joined:** Sun, 29 Nov 2009 00:24:43 UTC **Posts:** 40

If

is a square matrix of order

, then prove that
$det(\lambda I-A)=\lambda ^n-tr(A)\lambda ^{n-1}+P_{n-2}(\lambda)$
with $P_{n-2}$ is the polynomial of order (teh greatest) $n-2\text{ in }\lambda$

Matt · **Joined:** Wed, 1 Oct 2003 04:45:43 UTC **Posts:** 9642

This amounts to showing that tr(A) is the sum of the roots of the characteristic polynomial (or the sum of the eigenvalues of A).

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Prove, about characteristic polynomial...

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