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- Jan 29, 2012

- 661

Here is a link to the question:his problem is about diagonalization of matrices A which have n mutually orthogonal eigenvectors, each of which has length one. It is customary to write U for the matrix with columns constructed from the eigenvectors. The problem is straightforward, but requires you to follow a given suggestion. Here is the problem, followed by the suggestion.

Suppose A = UDU^-1;

where D is diagonal and U is given as above. The entries of D; U are real numbers. Show that A is equal to its transpose matrix.

Suggestion: In the diagonalization formula for A, replace U^-1 by U^T (this is valid for such matrices) and then take the transpose of both sides. Compare.

In the literature, A is called symmetric, and U is called orthogonal.

Diagnalization with matrices? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.