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)
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.
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 ) .
Use that if then, .b)Let A is a realnumber matrix nxn. Show that det (exp (A)) = det (exp (J)) where J isthe Jordan canonical form of A.
Said well, support you ！
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