Linear Algebra

by Juan Jorge Schaffer

Overview

In the spirit of the author’s Basic Language of Mathematics, this companion volume is a careful exposition of the concepts and processes of Linear Algebra. It stresses cautious and clear explanations, avoiding reliance on co-ordinates as much as possible, and with special, but not exclusive, attention to the finite-dimensional situation. It is intended to also serve as a conceptual and technical background for use in geometry and analysis as well as other applications.

Product Details

ISBN-13:	9789814623490
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	09/30/2014
Pages:	140
Product dimensions:	6.50(w) x 9.80(h) x 0.60(d)

Table of Contents

Preface v

Chapter 1 Linear Spaces and Linear Mappings

11 Linear spaces 1

12 Linear mappings 6

13 Subspaces 11

14 Linear partitions 20

15 Supplements 24

Chapter 2 Properties of Linear Mappings

21 Linear invertibility 29

22 Cancellability and factorization 34

Chapter 3 Linear Products and Coproducts

31 Linear products 39

32 Linear coproducts 44

33 Decompositions 49

Chapter 4 Families in Linear Spaces

41 Linear combination 57

42 Linear' independence 60

43 Linear independence, spanning, bases 65

Chapter 5 Finite Dimension

51 Matrices 73

52 Finite-dimensional spaces 77

53 Finite dimension and linear mappings 83

54 Finite- and infinite-dimensional spaces 90

Chapter 6 Duality

61 Dual spaces and transposes 93

62 Annihilators 97

63 Higher-order dual spaces and transposes 106

64 Biortliogonal families 110

Chapter 7 Duality and Finite Dimension

71 Duality for finite-dimensional spaces 113

72 Dual bases and matrices 117

73 The trace form 121

74 The canonical identifications 127

Indexes

Index of terms 129

Index of symbols 131