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Re: Finding equivalent matrix
Posted:
Oct 22, 2009 12:33 PM


> 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.



