## Quadratic forms

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, ax2+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.