The Quadratic Form

A quadratic form is a mathematical expression where you take a set of variables, multiply each by a number representing their relationships, and combine these products in a specific way. Often written as \(x^T A x\), where \(x\) is a vector of variables and \(A\) is a matrix, it essentially measures certain properties of the variables, like their combined size or interaction. Quadratic forms are used in areas like optimization, statistics, and physics to understand how variables relate to each other in a structured, consistent manner.