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" Linear Algebra "
by Werner H. Greub.
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BL
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| Record Number
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759069
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b579040
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| Main Entry
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by Werner H. Greub.
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| Title & Author
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Linear Algebra\ by Werner H. Greub.
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| Edition Statement
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Second Editon
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| Publication Statement
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Berlin, Heidelberg : Springer Berlin Heidelberg, 1963
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| Series Statement
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Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete, 97.
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(xi, 338 pages)
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| ISBN
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3662015455
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: 9783662015452
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| Contents
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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.
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| Abstract
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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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Mathematics.
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Werner H Greub
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