The orthogonal matrix and its applications

The subject of matrices and their applications is of great importance, for this branch of mathematics, perhaps more than any other, has been applied to numerous diversified fields, namely, to education, psychology, chemistry, physics, electrical, mechanical, and aeronautical engineering, statistics, and economics. Its importance lies in its use as a "tool" for the mathematician as well as those engaged in other fields. As one would expect, some phases of this theory, such as the theories of quadratic forms and symmetric matrices, are more highly developed than others because of their importance in the study of conic sections and quadric surfaces, in problems of maxima and minima, and in dynamics and statistics. In this paper, the basic theorems and properties of orthogonal matrices have been set forth and discussed, however, although some theorems on general matrix theory have been used in proofs leading to and including orthogonal matrices, no proofs of these theorems have been presented but they can be found in almost any book on matrix theory