ABSTRACT
An important occurrence of matrices comes from linearizing dependences. When certain quantities depend on several quantities, and not just one variable, the corresponding rates of change naturally form a matrix. Mathematical properties of this matrix reveal a lot about the dependence. When maximizing functions of one variable, we often looked at the second derivative. In a situation when a function depends on several variables, the second derivatives would form a matrix, called the Hessian. This construction, and related bordered Hessian matrices, play an important role in optimization theory.
