Linear Algebra PDF

by Werner H. Greub

Part of the Grundlehren der mathematischen Wissenschaften series

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Description

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.