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Linear AlgebraHardSingular Values & the SVD

Singular Values & the SVD · Hard problem

Let A=(403−5)A = \begin{pmatrix}4 & 0\\3 & -5\end{pmatrix}. What fraction of ∥A∥F2\|A\|_F^2 (the total "energy") is captured by its best rank-one approximation A1A_1, i.e. find ∥A1∥F2/∥A∥F2\|A_1\|_F^2/\|A\|_F^2?