Quadratic form

A function that can be written as xv^Tv Cx,v where the n × n matrix Cv is a matrix of known coefficients and xv is a column vector. Matrix Cv is usually assumed to be symmetric or can be transformed into a symmetric martrix. The form is said to be positive definite if xv^Tv Cxv > 0 for xv ≠ 0. The form is positive semidefinite if xv^Tv Cxv ≥ 0 for all x.v Negative definite and negative semidefinite forms are defined by appropriate reversal of the inequality signs in the preceding definitions. Matrices and matrix algebra.