Linear, Bilinear, and Quadratic Forms

Abstract

This chapter is devoted to certain functions (of an n-dimensional vector) that are defined in Section 14.1 and that are known as linear, bilinear, and quadratic forms. Those bilinear forms that have certain properties (known as symmetry and positive definiteness) are of interest (at least in part) because they qualify as inner products for R n (as is discussed in Section 14.10). Quadratic (and bilinear) forms are of considerable relevance in statistics; the “sums of squares (or products)” in an analysis of variance (or covariance) table are quadratic (or bilinear) forms.