Category:Definitions/Positive Definite Matrices

This category contains definitions related to Positive Definite Matrices.
Related results can be found in Category:Positive Definite Matrices.

Let $\mathbf A$ be a symmetric square matrix of order $n$.

Definition 1

$\mathbf A$ is positive definite if and only if:

for all nonzero column matrices $\mathbf x$ of order $n$, $\mathbf x^\intercal \mathbf A \mathbf x$ is strictly positive.

Definition 2

$\mathbf A$ is positive definite if and only if:

all the eigenvalues of $\mathbf A$ are strictly positive.