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*Then there exists a factorization, called a singular value decomposition of A, of the form
*Then there exists a factorization, called a singular value decomposition of A, of the form
where
where
U is an m × m unitary matrix,
U is an m × m unitary matrix,
S is a diagonal m × n matrix with non-negative real numbers on the diagonal,
S is a diagonal m × n matrix with non-negative real numbers on the diagonal,
V is an n × n unitary matrix over K, and
V is an n × n unitary matrix over K, and
<math>V^T</math> is the conjugate transpose of V.
<math>V^T</math> is the conjugate transpose of V.