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Exercise 1.12.4

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With fixed $V$ , we can do the same process but using the rows of the matrix $A - UV$ since the Frobenius norm is not related to row or column order. The $u$ that minimize $| | A - UV | |_{F}^{2}$ is: $v v^{T} u_{1} = a_{1}^{T} v^{T}$ , where $a_{1}^{T}$ is the first row of $A$ .

In vector form, the best $u$ solves $(v v^{T}) u = A v^{T}$ .

niuers

2020-03-20 00:00

Exercise 1.12.4

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