Orthogonal transformation of matrix

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The discussion focuses on the properties of the 2-norm in relation to orthogonal transformations of matrices. It asserts that the 2-norm remains invariant under orthogonal transformations, specifically when Q is orthogonal and satisfies Q^T*Q=I. The challenge lies in demonstrating that the equation || Q^H*A*Q ||2 = || A ||2 holds true for orthogonal matrices Q and Q^H. The 2-norm is defined as the square-root of the maximum absolute eigenvalues of A^HA, prompting the need to verify whether the transformation (Q^HA*Q)^HQ^HA*Q maintains the absolute eigenvalues of A^HA. This inquiry highlights the relationship between orthogonal transformations and matrix norms in linear algebra.
vabamyyr
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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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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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