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Einführung in die Determinantentheorie: einschliesslich der Fredholmschen Determinanten
Gerhard Kowalewski
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AMS Chelsea Publishing
1945; 320 pp; hardcover
ISBN-10: 0-8284-0039-3
ISBN-13: 978-0-8284-0039-8
List Price: US$42
Member Price: US$37.80
Order Code: CHEL/39
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This is the third edition of Kowalewski's classic treatise on determinants. The majority of the book concerns properties of determinants of matrices, including special families of matrices, such as symmetric or orthogonal matrices. A main chapter covers the applications to linear and quadratic forms. Kowalewski then turns his attention to matrices associated to one or more functions. An example of such is the Wronskian of a collection of \(n\) functions of one variable, which is connected with the theory of \(n\)th-order ordinary differential equations. Another key example is that of the Fredholm determinant and the associated minors, which are important in Hilbert's approach to the solution of linear integral equations. The third edition finishes with a newly added chapter on elementary divisor theory.

Reviews

"[A] classic in its field ... excellent treatise ... remarkably elegant and lucid ... Open the book where you will and you will find yourself in the midst of a live question having vital connections with other live branches of mathematics ... The choice of subjects ... has been guided by a true sense of values, not by a mere love of formal developments ... The detailed exposition of the proof is always good and frequently a model of clearness and conciseness; it is evident that we have to deal with a writer whose expositionary powers are of the first order."

-- Bulletin of the AMS

Table of Contents

  • Historische Bemerkungen
  • Definition der \(n\)-reihigen Determinante
  • Einfachste Eigenschaften der Determinanten
  • Unterdeterminanten
  • Systeme linearer Gleichungen
  • Multiplikation von Matrizen und Determinanten
  • Determinanten, deren Elemente Minoren einer andern sind
  • Symmetrische Determinanten
  • Schiefsymmetrische Determinanten
  • Orthogonale Determinanten
  • Resultanten und Diskriminanten
  • Lineare und quadratische Formen
  • Funktionaldeterminanten
  • Wronskische und Gramsche Determinanten
  • Einige geometrische Anwendungen der Determinanten
  • Die linearen Integralgleichungen
  • Elementarteilertheorie
  • Literaturnachweise und Anmerkungen
  • Sachregister
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