Positive-definite matrix

A positive-definite matrix is a matrix with special properties. The definition of the term is best understood for square matrices that are symmetrical, also known as Hermitian matrices. 
Definition.
A square matrix filled with real numbers is positive definite if it can be multiplied by any non-zero vector and its transpose and be greater than zero. The vector chosen must be filled with real numbers.
Examples.
when the entries "z"0, "z"1 are real and at least one of them nonzero, this is positive. This proves that the matrix formula_4 is positive-definite.