ABSTRACT
A quadratic form is given by the expression x ′ Ax where x is an n × 1 vector and A an n × n matrix. Quadratic forms arise in various branches of economics, and particularly in optimization theory to identify a candidate solution as a maximum or minimum. For example, in the study of quadratic functions, ax 2 + bx + c = (ax + b)x + c, this function is either “u-shaped” or the opposite, depending on whether a is positive or negative. So, the turning point either locates a minimum or a maximum depending of the sign of a. If, for example, a > 0, then large values of x correspond with large values of the function and the turning point corresponds to a minimum value of the function.
