Question: are symmetric matrices positive definite?
Answer: Definition: The symmetric matrix A is said positive definite (A > 0) if all its eigenvalues are positive. Definition: The symmetric matrix A is said positive semidefinite (A ≥ 0) if all its eigenvalues are non negative. ... Theorem: A is positive definite if and only if xT Ax > 0, ∀x ̸= 0.