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Positive-semi-definite matrix

  1. Nov 19, 2008 #1
    [tex]A*A^T[/tex]

    Will result in a symmetric matrix. Does this mean that A*A^T will be positive semi-definite?


    Does A have to be strictly real, can it be complex?
     
  2. jcsd
  3. Nov 20, 2008 #2

    D H

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    A*AT is symmetric IF A is real. For complex matrices you want to use the adjoint rather than the transpose.

    The eigenvalues of A*A* are always real and non-negative. The square roots of these eigenvalues are called the singular values of A. Singular value decomposition is a very important matrix decomposition technique.
     
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