orthogonal transformation of matrix

by vabamyyr
Tags: matrix, orthogonal, transformation
vabamyyr is offline
Apr6-06, 04:34 PM
P: 66
I have a question on matrix norms and orthogonal transformations. The 2-norm in invariant under orthogonal transformation, for if Q^T*Q=I. But i have trouble showing that for orthogonal Q and Q^H with appropriate dimensions

|| Q^H*A*Q ||2 =|| A ||2
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doodle is offline
May23-06, 07:49 AM
P: 161
The 2-norm of A returns the square-root of the maximum absolute eigenvalues of A^HA. So check, does (Q^HA*Q)^HQ^HA*Q preserve the absolute eigenvalues of A^HA?

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