A Treatise On The Theory Of Determinants

One of the few comprehensive single-volume treatments of determinants, this compilation features nearly all of the known facts about determinants up to the early 1930s. The text begins with the basic elements of permutations and combinations and sets down the notation and general principles of simple determinants, with a full discussion of such topics as row and column transformation, expansion, multiplication, minors, and symmetry. Additional topics include compound determinants, co-factors, adjugates, rectangular arrays and matrices, linear dependence, and many more subjects. Although its primary focus is upon answering reference and research needs, this book's 485 problems (plus scores of numerical examples) make it extremely useful to students and teachers.

Reprint of the original, first published in 1880.

This classic text on the theory of determinants has stood the test of time, remaining an essential reference for mathematicians and scientists today. With clear explanations of complex concepts and detailed examples of applications, Thomas Muir provides readers with the tools they need to explore this fundamental area of mathematics. A must-read for anyone interested in algebraic theory. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Excerpt from A Treatise on the Theory of Determinants: With Graduated Sets of Exercises, for Use in Colleges and Schools I have here attempted to do for Determinants what has been already often enough done for various other branches of Mathematics, viz. To produce a text-book containing a full exposition of the theory in a form suitable for students, and having at intervals graduated collections of exercises to test the reader's progress and to prepare him for the succeeding stage of the subject. The First Chapter refers to determinants of the second, third, and fourth orders, but only by way of introduction to what follows, and is written in the simplest possible style. The reader who has already some acquaintance with general algebraical reasoning may pass it over. The Second Chapter treats of determinants in general and gives in one form or another all their important properties. At first, in the demonstrations recurrence is made to the definition oftener than is necessary for the purpose of mere proof, in order that thereby the reader may become thoroughly familiarized with the definition itself, which of course really contains the whole matter. For a similar reason the properties given towards the commencement are somewhat spread out and dwelt upon. Afterwards, the style becomes gradually more condensed to suit the advancing stage of the reader's knowledge. 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.