Theorem: trace(X X^T) - 13 = 0 at X = diag(2, 3) (SVD Frobenius-norm-squared)

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Theorem (SVD-Frobenius-trace canonical): for X = diag(2, 3), the singular values are sigma_1 = 3, sigma_2 = 2 (sorted descending), and the Frobenius norm squared is ||X||_F^2 = sigma_1^2 + sigma_2^2 = 9 + 4 = 13. Equivalently trace(X X^T)…

Related concepts

Least-squares via SVD: beta-hat = V Sigma^+ U^T y; Frobenius-norm extremum
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