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Linear Algebra : A Pure Mathematical Approach by Harvey E. Rose (2002, Perfect)

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About this product

Product Identifiers

PublisherSpringer Basel A&G

ISBN-10376436792X

ISBN-139783764367923

eBay Product ID (ePID)23038414408

Product Key Features

Number of PagesXiv, 250 Pages

LanguageEnglish

Publication NameLinear Algebra : a Pure Mathematical Approach

SubjectAlgebra / Linear

Publication Year2002

TypeTextbook

Subject AreaMathematics

AuthorHarvey E. Rose

FormatPerfect

Dimensions

Item Height0.2 in

Item Weight18.7 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2002-026037

Reviews"Rose's Linear Algebra is a highly sophisticated undergraduate work . . . This book would be excellent for mathematics majors or for non-majors with access to a second course in which applications were presented. Summing Up: Recommended for lower- and upper-division undergraduates." ?CHOICE

Dewey Edition21

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal512/.5

Table Of Content1 -- Algebraic Preamble.- Groups, Rings and Fields.- Permutation Groups.- Problems 1.- 2 -- Vector Spaces and Linear Maps.- Vector Spaces and Algebras.- Bases and Dimension.- Linear Maps.- Direct Sums.- Addendum - Modules.- Problems 2.- 3 -- Matrices, Determinants and Linear Equations.- Matrices.- Determinants.- Systems of Linear Equations.- Problems 3.- 4 -- Cayley-Hamilton Theorem and Jordan Form.- Polynomials.- Cayley-Hamilton and Spectral Theorems.- Jordan Form.- Problems 4.- 5 -- Interlude on Finite Fields.- Finite Fields.- Applications - Linear Codes and Finite Matrix Groups.- Problems 5.- 6 -- Hermitian and Inner Product Spaces.- Hermitian and Inner Products, and Norms.- Unitary and Self-adjoint Maps.- Orthogonal and Symmetric Maps.- Problems 6.- 7 -- Selected Topics.- The Geometry of Real Quadratic Forms.- Normed Algebras, Quaternions and Cayley Numbers.- to the Representation of Finite Groups.- Problems 7.- Appendix A -- Set Theory.- Sets and Maps.- Problems A.- Appendix B -- Answers and Solutions to the Problems.- Notation Index.- Definition Index.- Theorem Index.

SynopsisLinear algebra is one of the most important branches of mathematics, because of its applications to other areas of mathematics, and because it encompasses ideas and results which are basic to pure mathematics. This book introduces to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach. Many examples, exercises and problems are provided, with answers or sketch solutions given in an appendix., In algebra, an entity is called linear if it can be expressed in terms of addition, and multiplication by a scalar; a linear expression is a sum of scalar multiples of the entities under consideration. Also, an operation is called linear if it preserves addition, and multiplication by a scalar. For example, if A and Bare 2 x 2 real matrices, v is a (row) vector in the real plane, and c is a real number, then v(A + B) = vA + vB and (cv)A = c(vA), that is, the process of applying a matrix to a vector is linear. Linear Algebra is the study of properties and systems which preserve these two operations, and the following pages present the basic theory and results of this important branch of pure mathematics. There are many books on linear algebra in the bookshops and libraries of the world, so why write another? A number of excellent texts were written about fifty years ago (see the bibliography); in the intervening period the 'style' of math ematical presentation has changed. Also, some of the more modern texts have concentrated on applications both inside and outside mathematics. There is noth ing wrong with this approach; these books serve a very useful purpose. But linear algebra contains some fine pure mathematics and so a modern text taking the pure mathematician's viewpoint was thought to be worthwhile., In algebra, an entity is called linear if it can be expressed in terms of addition, and multiplication by a scalar; a linear expression is a sum of scalar multiples of the entities under consideration. Also, an operation is called linear if it preserves addition, and multiplication by a scalar. For example, if A and Bare 2 x 2 real matrices, v is a (row) vector in the real plane, and c is a real number, then v(A + B) = vA + vB and (cv)A = c(vA), that is, the process of applying a matrix to a vector is linear. Linear Algebra is the study of properties and systems which preserve these two operations, and the following pages present the basic theory and results of this important branch of pure mathematics. There are many books on linear algebra in the bookshops and libraries of the world, so why write another? A number of excellent texts were written about fifty years ago (see the bibliography); in the intervening period the 'style' of math- ematical presentation has changed. Also, some of the more modern texts have concentrated on applications both inside and outside mathematics. There is noth- ing wrong with this approach; these books serve a very useful purpose. But linear algebra contains some fine pure mathematics and so a modern text taking the pure mathematician's viewpoint was thought to be worthwhile.

LC Classification NumberQA184-205