Multivariate Statistical Analysis: The Geometric Theory

This paper presents a new geometric approach to the multivariate statistical analysis. In essence, this geometric theory replicates the classical one-dimensional theory. As a tool for this generalization, an extended version compared to the classical linear algebra was developed. In this version, squared matrices are used as scalar products of elements. In terms of this generalized linear algebra, general concepts of linear models and linear hypotheses are given; a matrix-valued least squares method is given, and its relation to the classical one is discussed; a general method for testing linear statistical hypotheses in a geometric, coordinate-free form is developed.