Some of the things I've learned every day since Oct 10, 2016
57: Positive-Definite Matrices
December 6, 2016Posted 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