Matrices and Determinoids:, Volume 1

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Cambridge University Press, Mar 28, 2013 - Mathematics - 444 pages
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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
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