# Matrices and Determinoids:, Volume 1

Cambridge University Press, Mar 28, 2013 - Mathematics - 444 pages
Originally published in 1913, this book forms part of a three-volume work created to expand upon the content of a series of lectures delivered at the University of Calcutta during the winter of 1909-10. The chief feature of all three volumes is that they deal with rectangular matrices and determinoids as distinguished from square matrices and determinants, the determinoid of a rectangular matrix being related to it in the same way as a determinant is related to a square matrix. An attempt is made to set forth a complete and consistent theory or calculus of rectangular matrices and determinoids. The first volume contains the most fundamental portions of the theory and concludes with the solution of any system of linear algebraic equations, which is treated as a special case of the solution of a matrix equation of the first degree.

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### Contents

 CHAPTER 1 Determinoid deﬁned as an algebraical sum of complete derived 12 Some simple properties of determinoids 1921 19 The sign of a derived product is independent of the order of arrange 47 moves affects of derived sequences 55 CHAPTER IV 86 Theorems concerning the affects of complementary corranged derived 102 Reciprocal matrices and reciprocal determinoids 110111 110
 Product of three matrices taken in prescribed order reduction 184 Special cases of a standard product formed by a chain of matrix 207 one factor a unit matrix one factor a scalar matrix 219 activities are not equal 232244 243 of a product 253 Reciprocal and conjugate reciprocal of a standard product of square 261 RANK OF A MATRIX AND CONNEGHONS BETWEEN 265 Changes in the value of a determinoid due to inversions in the orders 286

 Expansion of a determinoid in terms of the simple minor determinants 116 Algebraical sum of the products obtained from two ﬁxed complementary 138 CHAPTER VI 153 Properties of the passive rows in a product of two matrices partial 164 equivalence of con 173
 Rank of a functional matrix and connections between its rows 294 The equations XA X+AB 300301 300 CHAPTER XI 364 INDEX 419 Copyright