7. Singular value decomposition
Singular value decomposition (SVD) has important applications in a wide variety of scientific fields. This decomposition can be seen as a generalization of the spectral decomposition of a Hermitian matrix, which is a decomposition of A into a product of the form A = U DU H where U is unitary and D diagonal. However, the SVD decomposition exists for any matrix, even in the case of rectangular matrices.
Theorem 13
For any matrix , there exist orthogonal matrices
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Singular value decomposition
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