Matrices and Determinoids:, Volume 2

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Cambridge University Press, Mar 28, 2013 - Mathematics - 580 pages
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Originally published in 1918, 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 second volume contains further developments of the general theory, including a discussion of matrix equations of the second degree. It also contains a large number of applications to algebra and to analytical geometry of space of two, three and n dimensions.
 

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Contents

CHAPTER
1
The primaries of a minor determinant horizontal and vertical
13
CHAPTER XIII
37
Possible simultaneous values of the paratomy cross rank
62
identities which
73
Criteria for the equivalence of two systems of linear algebraic
80
the funda
90
lb Relations between the minor determinants of order 1 of a matrix
98
equation and rank 1 in the second and third equations general
352
Expressions for a symmetric matrix of order 2 as a product of
365
Expressions for a symmetric matrix whose rank does not exceed 2
373
they
398
Reduction of an undegenerate matrix of extravagance p to
412
PAGES
432
Unconnected mutually orthogonal solutions of any system of homo
440
their
446

CHAPTER XIV
107
CHAPTER XV
165
the rank of
177
they have the same
183
CHAPTER XVI
228
A more general unitary transformation converting the matrix into
252
A corresponding nonunitary equigradent transformation 260264
260
rank r general solutions of the first two equations formulae
274
defined
295
Possible values of the rank and extravagance of a spacelet of homo
456
Possible values of the cross rank and mutual orthotomy of
463
Possible values of the cross rank and mutual orthotomy of two non
474
a APPENDIX A Utility of the relations obtained in Chapter XIII 515520
515
as a rational function of degree 1 of any one regular simple
518
130a APPENDIX B The Pfaffian of a skewsymmetric matrix of even
521
175a APPENDIX C Equigradent transformations in which one of
531
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