Editing Definite matrix (section)

=== Cholesky decomposition ===
A Hermitian positive semidefinite matrix <math>M</math> can be written as <math>M = L L^*,</math> where <math>L</math> is lower triangular with non-negative diagonal (equivalently <math>M = B^*B</math> where <math>B = L^*</math> is upper triangular); this is the [[Cholesky decomposition]].
If <math>M</math> is positive definite, then the diagonal of <math>L</math> is positive and the Cholesky decomposition is unique. Conversely if <math>L</math> is lower triangular with nonnegative diagonal then <math>L L^*</math> is positive semidefinite. 
The Cholesky decomposition is especially useful for efficient numerical calculations.
A closely related decomposition is the [[Cholesky decomposition#LDL decomposition|LDL decomposition]], <math>M = L D L^*,</math> where <math>D</math> is diagonal and <math>L</math> is [[Triangular matrix#Unitriangular matrix|lower unitriangular]].