Inner Products, Projections and the SVD · 免费预览

矩阵逼近

1. Matrix Approximation

Matrix Approximation

The best rank- $k$ approximation of $A$ in the spectral norm is obtained by

Matrix Approximation (2)

Matrix Approximation (3)

Matrix Approximation (4)

Matrix Approximation (5)

Matrix Approximation (6)

Matrix Approximation (7)

For the rank- $k$ truncation $A_k$ , the Frobenius-norm error $\|A - A_k\|_F$ equals

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