Linear Algebra : A Pure Mathematical Approach

Harvey E. Rose

ISBN 10: 376436792X / ISBN 13: 9783764367923

Published by Birkhäuser, Birkhäuser, 2002

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783764367923

Bibliographic Details

• Title: Linear Algebra : A Pure Mathematical Approach
• Publisher: Birkhäuser, Birkhäuser
• Publication Date: 2002
• Language: English
• ISBN 10: 376436792X
• ISBN 13: 9783764367923
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 15D millimeters 235 millimeters width by 155 millimeters height by 15 millimeters depth
• Weight: 411 grams

About this title

Synopsis

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.

About the Author

"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