Greub Linear Algebra

2. Auflage 1963
ISBN: 978-3-662-01545-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 338 Seiten, Web PDF

Reihe: Mathematics and Statistics (R0)

Besides the very obvious change from German to English, the second edition of this book contains many additions as weil as a great many other changes. It might even be called a new book altogether were it not for the fact that the essential character of the book has remained the same; in other words, the entire presentation continues to be based on an axiomatic treatment of linear spaces. In this second edition, the thorough-going restriction to linear spaces of finite dimension has been removed. Another complete change is the restriction to linear spaces with real or complex coefficients, thereby removing a number of relatively involved discussions which did not really contribute substantially to the subject. On p.6 there is a list of those chapters in which the presentation can be transferred directly to spaces over an arbitrary coefficient field. Chapter I deals with the general properties of a linear space. Those concepts which are only valid for finitely many dimensions are discussed in a special paragraph. Chapter 11 now covers only linear transformations while the treat ment of matrices has been delegated to a new chapter, chapter 111. The discussion of dual spaces has been changed; dual spaces are now intro duced abstractly and the connection with the space of linear functions is not established untillater.

Zielgruppe

Research

Autoren/Hrsg.

Greub, Werner H.

Inhaltsverzeichnis

I. Linear spaces.- II. Linear transformations.- III. Matrices.- IV. Determinants.- V. Oriented linear spaces.- VI. Multilinear mappings.- VII. Tensor-algebra.- VIII. Exterior algebra.- IX. Duality in exterior algebra.- X. Inner product spaces.- XI. Linear mappings of inner product spaces.- XII. Symmetric bilinear functions.- XIII. Quadrics.- XIV. Unitary spaces.- XV. Invariant subspaces.