CODEWITHSUNDEEP
matrix-multiplicationeigensvdsquare-root
ALFRAM
ALFRAM

Reputation: 193

Svd and Eigen decomposition of Matrices

My question is about Singular Value and Eigen Decomposition for any matrices. For any matrice A, let say my SVD is A = UDW' and my Eigen Decomposition is A = BCinv(B). Let take a real number x, under some assumptions A^(x) = B.C^(x)inv(B). How can I obtain A^(x) with SVD decomposition?

Thanks

Upvotes: 0

Views: 632

Answers (1)

SpamBot
SpamBot

Reputation: 1458

I believe you would like to construct some real power of a matrix A, A^(x) = B C^(x) inv(B), where B C inv(B) can be obtained by eigen decomposition. The short answer is that the matrices U, W given by a singular value decomposition are usually not the inverse of each other https://math.stackexchange.com/a/320232. That is, they would not "cancel out" in the constructed matrix power function. There is no clear way how to contruct a real matrix power function with SVD.

Only when A is symmetric, SVD becomes similar to an eigen decomposition (up to permuting the values). But then you could well stick to eigen decomposition.

Upvotes: 1

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