Consider the 4×5 matrix
A singular value decomposition of this matrix is given by
Notice is zero outside of the diagonal and one diagonal element is zero. Furthermore, because the matrices and are unitary, multiplying by their respective conjugate transposes yields identity matrices, as shown below. In this case, because and are real valued, they each are an orthogonal matrix.
This particular singular value decomposition is not unique. Choosing such that
is also a valid singular value decomposition.
Read more about this topic: Singular Value Decomposition
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4 ... Next we have to scale the structures up by increasing m ...
... Then the projection on the first component of a distribution's wave front set is nothing else than its classical singular support, i.e ... the complement of the set on which its restriction would be a smooth function ...
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