Positive definite matrices

Every positive-definite symmetric matrix is a covariance matrix, and vice-versa. This is just one application of the theory of positive-definite matrices. In this talk, I will give an introduction to the mathematics of positive-definite matrices. I will demonstrate their analogy to positive real numbers by presenting the polar decomposition. I hope then to discuss Choi's theorem on completely positive maps and mention its relevance to quantum information theory.