If $A$ is a square $m \times m$ matrix and $O$ is an orthogonal $m \times m$ matrix, is it true that $$\|AO \|_F=\|A\|_F,$$ where $\|\cdot\|_F$ stands for the Frobenius norm of the matrix?
Is the Frobenious norm of a matrix orthogonally invariant?
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real-analysis
matrices
norm
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2By the Frobenius norm, you presumably mean $\|A\|_{F}^{2} := \operatorname{tr}(A^{t}A)$...? If so, can you say where you're stuck? – 2017-01-10
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1The Frobenius norm is the square root of the sum of the squares of the norms of the columns. An orthogonal matrix preserves the norms of columns (which are just vectors). – 2017-01-10
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1Ok, thanks @ Andrew D. Hwang and @juan arroyo, I get it now... – 2017-01-10