Page "Positive-definite matrix" Paragraph 43

For any matrix A, the matrix A < sup >*</ sup > A is positive semidefinite, and rank ( A ) = rank ( A < sup >*</ sup > A ).

Conversely, any Hermitian positive semidefinite matrix M can be written as M = A < sup >*</ sup > A ; this is the Cholesky decomposition.