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Excerpt from Homogeneous Linear Substitutions
In this book I have attempted to put together for the benefit of the mathematical student those properties of the Homogeneous Linear Substitution with real or complex coefficients of which frequent use is made in the Theory of Groups and in the Theory of Bilinear Forms and Invariant-factors; but which have not hitherto been collected in a single treatise, so far as I am aware.
I have confined myself to those properties of substitutions which do not depend on any group of such substitutions. The main reason for this limitation is the fact that the most interesting properties of substitution-groups may be found in the second edition of Prof. Burnside's Theory of Groups (Cambridge Univ. Press, 1911); and it does not seem worth while to repeat work already so excellently performed. I have also limited myself in the main to the discussion of substitutions whose determinant does not vanish.
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Homogeneous Linear Substitutions (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book explores the concept of homogeneous linear substitution with real or complex coefficients, a topic that finds practical applications in group theory, the theory of bilinear forms, and invariant factor theory. The author examines properties of substitutions, including inverses, powers, and the concept of poles and characteristic equations, which aid in determining the characteristic roots of a substitution. The book discusses the various types of substitutions, such as normal, canonical, and orthogonal, and their uses. It also delves into the concept of invariants, or functions that remain unchanged under substitution transformations. Overall, this book provides a comprehensive understanding of the subject, making it a valuable resource for mathematicians and students seeking a deeper understanding of linear substitutions and their applications. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781332230716_0
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