The Theory of Matrices, Vol. 2 (Classic Reprint)


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Excerpt from The Theory of Matrices, Vol. 2 Determination of the index of an arbitrary rational frac tion by the coefficients of numerator and denominator. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.




Matrices and Determinoids, Vol. 2 (Classic Reprint)


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Excerpt from Matrices and Determinoids, Vol. 2 HE author's chief aim in writing this book was to give a systematic account of certain applications of matrices, particularly of, rectangular matrices as distinguished from square matrices, and thereby to illustrate the very great advantages gained by using them in almost all branches of Mathematics. It originated in a habit of using matrices freely in, the solu tion of problems in Algebra, Geometry and Applied Mathematics, and is based on the very extensive manuscript acquired in doing so. To give a satisfactory answer to the frequently propounded question 'what is a matrix it seemed advisable to commence with some account of the theory. Accordingly the course of Readership Lectures in which this work was first made public was divided into two halves, the first half dealing with the theory, and the second half with the applications. The theoretical portion has, been constantly increased, in the first place by abstractions from the applications, and in the second place by incorporating the work of other writers. As a consequence the applications have been driven further back, though they still remain the ultimate object of the book. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.




Applications of the Theory of Matrices


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The breadth of matrix theory's applications is reflected by this volume, which features material of interest to applied mathematicians as well as to control engineers studying stability of a servo-mechanism and numerical analysts evaluating the roots of a polynomial. Starting with a survey of complex symmetric, antisymmetric, and orthogonal matrices, the text advances to explorations of singular bundles of matrices and matrices with nonnegative elements. Applied mathematicians will take particular note of the full and readable chapter on applications of matrix theory to the study of systems of linear differential equations, and the text concludes with an exposition on the Routh-Hurwitz problem plus several helpful appendixes. 1959 edition.













The Theory of Matrices


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On the Roots of Matrices (Classic Reprint)


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Excerpt from On the Roots of Matrices In his memoir on Matrices (phil. Trans. 1858) Prof. Cayley enunciated the theorem: The determinant, having for its matrix a given matrix less the same matrix considered as a single quantity involving the matrix unity, is equal to zero. The equation implied in this theorem is known as Cayley's identical equation. Subsequently (in the Mess. Math. Vol. XIII, p. Mr. A. R. Forsyth gave a proof of this identical equation for matrices of the third order, based upon the solution of a system of linear difference equations.* Forsyth's method is applicable to matrices of any order. Considerable simplicity is gained, however, by the employment of non-scalar equations instead of the scalar equa tions employed by Forsyth. I have employed this modification of Forsyth's method to prove Sylvester's law of latency and Sylvester's theorem. In addition I have by this method investigated the existence of 'roots of matrices for different indices and in particular the roots of nilpotent matrices. For valuable suggestions in the working of this paper I am indebted to Dr. Henry Taber. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.




The Theory of Matrices


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A Treatise on the Mathematical Theory of Elasticity, Vol. 2 (Classic Reprint)


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Excerpt from A Treatise on the Mathematical Theory of Elasticity, Vol. 2 Theories of the behaviour of thin bodies, as of bodies in general, are of two kinds. Either they are founded on special hypotheses, or they start from the general equations of Elasticity. Before the time of N avier all writers on rods and plates naturally adopted the former method, after his time most valuable investigations will be found to proceed by way of the latter. His researches form the turning point in the history of special problems as in that of general theory. Nevertheless the persistence of the older theories after the discovery of the general equations had made more exact investigations possible, and even after they had been carried out, is one of the most noteworthy facts in the history of our subject'. We shall now trace briefly the development of the theory of thin rods and its applications, we shall then consider the theory of thin plates, and we shall conclude by noticing the theory of elastic stability. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.