Can singular value decomposition be used for complex matrices?

[Cyrus]

A*A^T

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?

 

[D H]

A*A^T 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.