Linear Algebra: A Geometric Approach (Chapman Hall/CRC Mathematics Series 7)

Linear Algebra: A Geometric Approach (Chapman Hall/CRC Mathematics Series 7)

By: E. Sernesi (author), James Montaldi (translator)Paperback

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Description

This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry, finishing with a chapter on transformation groups; Part II is on quadratic forms and their geometry (Euclidean geometry), including a chapter on finite subgroups of 0 (2). Each of the 23 chapters concludes with a generous helping of exercises, and a selection of these have solutions at the end of the book. The chapters also contain many examples, both numerical worked examples (mostly in 2 and 3 dimensions), as well as examples which take some of the ideas further. Many of the chapters contain "complements" which develop more special topics, and which can be omitted on a first reading. The structure of the book is designed to allow as much flexibility as possible in designing a course, either by omitting whole chapters or by omitting the "complements" or specific examples.

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Contents

Part I Affine geometry: vector spaces; matrices; systems of linear equations; some linear algebra; rank; determinants; affine space - (I) - (II); geometry of affine planes; geometry of affine space; linear maps; linear maps and matrices, affine changes of coordinates; linear operators; transformation groups. Part II Euclidean geometry: bilinear and quadratic forms; diagonalizing quadratic forms; scalar product; vector product; Euclidean space; unitary operators and isometries; isometries of the plane and of three-dimensional space; the complex case.

Product Details

  • publication date: 15/05/1993
  • ISBN13: 9780412406805
  • Format: Paperback
  • Number Of Pages: 384
  • ID: 9780412406805
  • weight: 535
  • ISBN10: 0412406802
  • translations: Italian

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