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hermitian_positive_semi-definite_matrix [2013/09/19 20:50] nikolaj |
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| - | ===== Hermitian positive semi-definite matrix ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $n\in\mathbb N$ | | ||
| - | | @#FFBB00: $ A \in \mathrm{it}(n) $ | | ||
| - | |||
| - | | @#55EE55: $ A \in \mathrm{HermitianMatrix}(n) $ | | ||
| - | |||
| - | | $ x \in \text{ColumnVector}(n,\mathbb C) $ | | ||
| - | |||
| - | | @#55EE55: $ A \in \mathrm{SquareMatrix}(n,\mathbb C) $ | | ||
| - | | @#55EE55: $ x^* A\ x \ge 0 $ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | If $B$ is real/complex, then $C=B^*B$ is Hermitian positive semi-definite. | ||
| - | === Reference === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Positive-definite_matrix|Positive-definite matrix]] | ||
| - | ==== Parents ==== | ||
| - | === Subset of === | ||
| - | [[Hermitian matrix]], [[General positive semi-definite matrix]] | ||
