[筆記] Convex Optimization 2015.10.14

Existen of SVD For any A∈Rm×n of rank r there exists U∈Rm×r,D∈diag(r×r),V∈Rn×r s.t. A=UDVT and VTV=Ir,UTU=Ir ⎡⎣⎢A⎤⎦⎥=⎡⎣⎢U⎤⎦⎥[D][VT] - Proof: ATA∈Rn×n is positive seidefinite, so there exists D∈Rr×r ,

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