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m →Decomposition: The cholesky section implied that all positive definite matrices were able to be decomposed into LL^* and did not specify that only Hermitian matrices were able to be decomposed this way |
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===Cholesky decomposition===
A Hermitian positive semidefinite matrix <math>M</math> can be written as <math>M = LL^*</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>LL^*</math> is positive semidefinite.
The Cholesky decomposition is especially useful for efficient numerical calculations.
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