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Topic: Finding equivalent matrix
Replies: 2   Last Post: Mar 12, 2013 3:21 AM

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HallsofIvy

Posts: 116
Registered: 1/19/06
Re: Finding equivalent matrix
Posted: Oct 22, 2009 12:33 PM
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> My textbook isn't really clear in this topic. Is
> there a fixed set of elementary operations for
> finding an equivalent matrix, or is it done purely by
> trial/error and logic?

Just find AN equivalent matrix? To find a matrix equivalent to matrix A, take any invertible matrix P and calculate P^{1}AP. That will be a matrix equivalent to A.

To find a diagonal matrix equivalent to (diagonalizable) matrix A, construct P by taking the eigenvectors of A as its columns. (A will have sufficient eigevectors if and only if it is diagonalizable.)

To find a "Jordan form" matrix equivalent to A, construct P by taking the eigenvectors and generalized eigenvectors as columns.



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