Definite matrix
= Definite matrix
{wiki=Definite_matrix}
In linear algebra, a definite matrix refers to a square matrix that has specific properties related to the positivity of its quadratic forms. The terminology typically includes several definitions: 1. **Positive Definite Matrix**: A symmetric matrix \\( A \\) is called positive definite if for all non-zero vectors \\( x \\), the following holds: \\\[ x^T A x > 0. \\\] This implies that all eigenvalues of the matrix are positive.