Extremes of Determinants and Optimality of Canonical Variables

Abstract

Extremes of quadratic forms have been presented by several authors (Okamoto, 1969; Rao, 1973; Seber, 1984). The obvious multivariate extension of the extreme of quadratic forms is the extreme of the determinants as well as the ratios of the determinants. In this paper we develop some supremums of the determinants and the ratios of the determinants. A new optimality and equations of canonical variables are obtained.

Keywords:

• quadratic form
• singular value
• canonical variable