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Linear Algebra

Author: Werner H Greub
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1963.
Series: Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete, 97.
Edition/Format:   eBook : Document : English : Second EditonView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Werner H Greub
ISBN: 9783662015452 3662015455
OCLC Number: 851377968
Description: 1 online resource (xi, 338 pages).
Contents: 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.
Series Title: Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete, 97.
Responsibility: by Werner H. Greub.

Abstract:

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.

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