positive definite


positive definite

[′päz·əd·iv ′def·ə·nət] (mathematics) A square matrix A of order n is positive definite if for every choice of complex numbers x1, x2, …, xn , not all equal to 0, where x̄j is the complex conjugate of xj . A linear operator T on an inner product space is positive definite if 〈 Tu, u 〉 is greater than 0 for all nonzero vectors u in the space.