This is an old revision of the document!
Hermitian positive semi-definite matrix
Definition
| $n\in\mathbb N$ |
| $ A \in \mathrm{it}(n) $ |
| $ A \in \mathrm{HermitianMatrix}(n) $ |
| $ x \in \text{ColumnVector}(n,\mathbb C) $ |
| $ A \in \mathrm{SquareMatrix}(n,\mathbb C) $ |
| $ x^* A\ x \ge 0 $ |
Discussion
If $B$ is real/complex, then $C=B^*B$ is Hermitian positive semi-definite.
Reference
Wikipedia: Positive-definite matrix
Parents
Subset of
