Show that, if is any complex-valued matrix, where is the trace.
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Originally Posted by Bruno J. Show that, if is any complex-valued matrix, where is the trace. where is the variable of A?
is a matrix with complex entries.
Originally Posted by Bruno J. is a matrix with complex entries. I am confused..how can you calculate the exponent of a matrix....
Matrix exponential - Wikipedia, the free encyclopedia
Let be a polynomial,if the eigenvalue of is , then the eigenvalue of is we may look as a polynomial series of (limit) note that: but is the eigenvalue of (regard it as polynomial) so
Last edited by ynj; Aug 18th 2009 at 05:08 PM.
Remember that not every matrix is diagonalizable! In the case where the matrix is diagonal then it is easy to show that the identity holds because if is one of the diagonal entries, the corresponding entry of will be .
I have changed my proof every matrix have eigenvalue, and my proof is not based on diagonalibility
Originally Posted by Bruno J. Show that, if is any complex-valued matrix, where is the trace. See here (2/3rd of the way down) CB
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