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.
Contents
Preface; 12. Compound matrices; 13. Relations between the elements and minor determinants of a matrix; 14. Some properties of square matrices; 15. Banks of matrix products and matrix factors; 16. Equigradient transformations of a matrix whose elements are constants; 17. Some matrix equations of the second degree; 18. The extravagances of matrices and of spacelets in homogeneous space; 19. The paratomy and orthotomy of two matrices and of two spacelets of homogeneous space; Index.
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