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IEVref: | 102-06-29 | ID: | |

Language: | en | Status: Standard | |

Term: | positive definite matrix | ||

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Definition: | Hermitian matrix such that, for any non-zero column matrix A with complex elements, the 1 × 1 matrix UU^{H} has a unique element which is real and positive: (AUU^{H})AU_{11} > 0Note 1 to entry: A symmetric matrix U^{T} > 0 for any non-zero column matrix AU with real elements. UNote 2 to entry: All eigenvalues of a positive definite matrix are positive. | ||

Publication date: | 2008-08 | ||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO | ||

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Note 1 to entry: A symmetric matrix ** A** with real elements is a positive definite matrix if

Note 2 to entry: All eigenvalues of a positive definite matrix are positive.