Quadratic form

A quadratic form is an expression that combines variables in pairs, such as $x^*Ax$ or $\sum_{i,j}c_i\overline{c_j}K_{ij}$.

Quadratic forms turn a collection of pairwise relationships into one number. In positive-definiteness questions, the requirement is that this number never become negative for any allowed set of weights.

See also: matrix, vector, positive definiteness, kernel..