Let be a polynomial of degree n in x with real coefficients. For any mxm matrix A, we define .

Show that, if and , then A must be invertible. [Hint: isolate Im from the equation P(A) = 0m]

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- Nov 27th 2009, 02:42 PM450081592Show that A must be invertible
Let be a polynomial of degree n in x with real coefficients. For any mxm matrix A, we define .

Show that, if and , then A must be invertible. [Hint: isolate Im from the equation P(A) = 0m] - Nov 27th 2009, 03:18 PMtonio
- Nov 27th 2009, 03:31 PM450081592
- Nov 27th 2009, 03:38 PMtonio
- Nov 27th 2009, 04:14 PM450081592
- Nov 27th 2009, 04:51 PM450081592
by the way what is

[2 0 0]

[0 2 0]

[0 0 2] -2 ? it's like the identity but it's 2 instead of 1, can the matrix subtract a number

For A =

[2 2 -1]

[-1 -1 1]

[2 4 -1] , compute , if , calculate P(A). Calculate .) Can you explan this,>? - Nov 28th 2009, 01:19 AMtonio