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hermitian_positive_semi-definite_matrix [2013/09/19 20:48] nikolaj |
hermitian_positive_semi-definite_matrix [2013/09/19 20:50] nikolaj |
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| | @#55EE55: $ A \in \mathrm{HermitianMatrix}(n) $ | | | @#55EE55: $ A \in \mathrm{HermitianMatrix}(n) $ | | ||
| - | | $ v \in \text{ColumnVector}(n,\mathbb C) $ | | + | | $ x \in \text{ColumnVector}(n,\mathbb C) $ | |
| | @#55EE55: $ A \in \mathrm{SquareMatrix}(n,\mathbb C) $ | | | @#55EE55: $ A \in \mathrm{SquareMatrix}(n,\mathbb C) $ | | ||
| - | | @#55EE55: $ x^* A x \ge 0 $ | | + | | @#55EE55: $ x^* A\ x \ge 0 $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| + | If $B$ is real/complex, then $C=B^*B$ is Hermitian positive semi-definite. | ||
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Positive-definite_matrix|Positive-definite matrix]] | Wikipedia: [[http://en.wikipedia.org/wiki/Positive-definite_matrix|Positive-definite matrix]] | ||
