Property of Eigenvalues

mvabhay · **Joined:** Sun, 17 Oct 2010 08:50:25 UTC **Posts:** 2

We were told(at collage) that if c* is the indeterminate of a charecteristic matrix A,then,|A|-c* is an eigenvalue.We were asked to prove this,but I cannot find any proof for this.Is this identity true at all?I cannot find it anywhere in the internet.

|A| is the determinent of A.

Thank you

outermeasure · **Posted:** Mon, 18 Oct 2010 00:48:58 UTC

mvabhay wrote:

We were told(at collage) that if c* is the indeterminate of a charecteristic matrix A,then,|A|-c* is an eigenvalue.We were asked to prove this,but I cannot find any proof for this.Is this identity true at all?I cannot find it anywhere in the internet.

|A| is the determinent of A.

Thank you

An eigenvalue of what?

The companion matrix A-c^*I

has eigenvalues $\lambda-c^*$ for each eigenvalue (with multiplicity) $\lambda$ of A. $\det A$ need not be an eigenvalue of A, so you must be talking about some other matrix.

mvabhay · **Joined:** Sun, 17 Oct 2010 08:50:25 UTC **Posts:** 2

Sorry for the trouble.It turns out I got the property wrong. :oops:

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Property of Eigenvalues

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