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Exercise 1.9.6

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If $S = QΛ Q^{T}$ is a symmetric positive definite matrix. Then all of its eigenvalues are positive, so $S = QΛ Q^{T}$ is actually a SVD form and $Λ$ is the singular value matrix, $Q$ is the singular vector matrix. So $q_{1} λ_{1} q_{1}^{T}$ is the closest rank-1 approximation to $S$ in the $L^{2}$ matrix norm $| | S | |_{2}$ if $λ_{1}$ is the largest eigenvalue.

niuers

2020-03-20 00:00

Exercise 1.9.6

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