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Linear AlgebraEasySingular Values & the SVD

Singular Values & the SVD · Easy problem

A matrix AA has singular values 44, 22 and 11. What fraction of ∥A∥F2\|A\|_F^2 is captured by its best rank-one approximation A1A_1? That is, find ∥A1∥F2∥A∥F2\dfrac{\|A_1\|_F^2}{\|A\|_F^2}.