Can anyone help me showing that

a)Let A is a realnumber matrix nxn. Show that tr (A) =sum of all eigenvalues of A.

b)Let A is a realnumber matrix nxn. Show that det (exp (A)) = det (exp (J)) where J is

the Jordan canonical form of A.

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- Dec 12th 2011, 09:54 AMmathsohardtrace, jordan carnonical form
Can anyone help me showing that

a)Let A is a realnumber matrix nxn. Show that tr (A) =sum of all eigenvalues of A.

b)Let A is a realnumber matrix nxn. Show that det (exp (A)) = det (exp (J)) where J is

the Jordan canonical form of A. - Dec 12th 2011, 10:36 AMSironRe: trace, jordan carnonical form
We know that

Now, have you any idea about the matrix of the linear map? (I would choose a base wherefore the matrix of the linear map is a diagonal matrix) - Dec 12th 2011, 10:47 AMmathsohardRe: trace, jordan carnonical form
I know TAT^-1 is D and D is the diagonal matrix whose diagonal entries are the eigenvalues of A. Hmm. I think I kind of getting it but I think I need a smoother answer please!

- Dec 12th 2011, 02:59 PMFernandoRevillaRe: trace, jordan carnonical form
**Siron**'s answer is correct for diagonalizable matrices in . In general:

Use that similar matrices have the same trace and is similar to its canonical form of Jordan (triangular matrix whose elements in the diagonal are__exactly__the eigenvalues of ) .

Quote:

b)Let A is a realnumber matrix nxn. Show that det (exp (A)) = det (exp (J)) where J isthe Jordan canonical form of A.

- Dec 13th 2011, 10:02 PMmdiendd123456Re: trace, jordan carnonical form
Said well, support you ！

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