# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 57: Positive-Definite Matrices

December 6, 2016

Posted by on A complex matrix is said to be **positive-definite** iff for every column vector , is real and positive. This is equivalent to the condition that all the eigenvalues of are positive.

Similarly, there are variations of positive-definiteness with analogous conditions:

positive-semidefinite real and non-negative non-negative eigenvalues

negative-semidefinite real and non-positive non-positive eigenvalues

negative-definite real and negative negative eigenvalues

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