Editing Matrix decomposition (section)

=== Cholesky decomposition ===
{{main|Cholesky decomposition}}
*Applicable to: [[square matrix|square]], [[symmetric matrix|hermitian]], [[positive-definite matrix|positive definite]] matrix <math>A</math>
*Decomposition: <math>A=U^*U</math>, where <math>U</math> is upper triangular with real positive diagonal entries
*Comment: if the matrix <math>A</math> is Hermitian and positive semi-definite, then it has a decomposition of the form <math>A=U^*U</math> if the diagonal entries of <math>U</math> are allowed to be zero
*Uniqueness: for positive definite matrices Cholesky decomposition is unique. However, it is not unique in the positive semi-definite case.
*Comment: if <math>A</math> is real and symmetric, <math>U</math> has all real elements
*Comment: An alternative is the [[LDL decomposition]], which can avoid extracting square roots.