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Linear AlgebraSuperchallengeSingular Values & the SVD

Singular Values & the SVD · Superchallenge problem

Find the Frobenius distance from A=(403−5)A = \begin{pmatrix}4 & 0\\3 & -5\end{pmatrix} to the set of 2×22\times 2 orthogonal matrices, min⁡QTQ=I∥A−Q∥F\min_{Q^{T}Q = I}\|A - Q\|_F. Give an exact answer.