Singular Value Decomposition (SVD) and Polar Form

@inproceedings{2009SingularVD,
  title={Singular Value Decomposition (SVD) and Polar Form},
  author={},
  year={2009}
}
  • Published 2009
In this section we assume that we are dealing with a real Euclidean space E. Let f :E → E be any linear map. In general, it may not be possible to diagonalize a linear map f . However, note that f∗ ◦ f is self-adjoint, since 〈(f∗ ◦ f)(u), v〉 = 〈f(u), f(v)〉 = 〈u, (f∗ ◦ f)(v)〉. Similarly, f ◦ f∗ is self-adjoint. The fact that f∗ ◦f and f ◦f∗ are self-adjoint is very important, because it implies that f∗ ◦ f and f ◦ f∗ can be diagonalized and that they have real eigenvalues. In fact, these… CONTINUE READING

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