Positive-semi-definite matrix

  • Thread starter Cyrus
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  • #1
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[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?
 

Answers and Replies

  • #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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