A positive-definite matrix A is a Hermitian matrix that, for every non-zero column vector v, where H is the conjugate transpose of v, which, in the case of only real numbers, is its transpose. A positive-definite matrix will have all positive eigenvalues. The identity matrix is an example of a positive definite matrix. Negative definite, positive semi-definite, and negative semi-definite matrices are defined in a similar manner, with semi-definite matrices including zero.