Aitken A.C. Determinants and Matrices

Oliver and Boyd, 1944. — 142 p.The notation of ordinary algebra is a convenient system of shorthand, a compact and well-adapted code for expressing the logical relations of numbers. The notation of matrices is merely a later development of this shorthand, by which certain operations and results of the earlier system can be expressed at still shorter hand. The rules of operation are so few and so simple, so like those of ordinary algebra, the notation of matrices is so concise yet so flexible, that it has seemed profitable to begin this book with a brief account of matrices and matrix algebra, and to derive the theory of determinants by the aid of matrix notation, in an order suggested by a naturally alternating development of both subjects. This first chapter is devoted to explaining the code. The reader is invited to take it with due deliberation, to invent at all times and verify examples for himself, especially in regard to the transposition of matrix products and to the multiplication of partitioned matrices, and, at first, to write out results both in ordinary and in matrix notation for comparison. The confidence and facility acquired by such practice will prove to be of constant service during the study of the later chapters.