1. A square matrix A of order n is positive definite if

for every choice of complex numbers x₁, x₂, ..., x_n , not all equal to 0, where x̄_j is the complex conjugate of x_j . 2. 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.