The primary purpose of this fourth edition of Linear Algebra is to present

a careful treatment of the principal topics of linear algebra and to illustrate

the power of the subject through a variety of applications. Our major thrust

emphasizes the symbiotic relationship between linear transformations and

matrices. However, where appropriate, theorems are stated in the more general infinite-dimensional case. For example, this theory is applied to finding

solutions to a homogeneous linear differential equation and the best approximation by a trigonometric polynomial to a continuous function.

Although the only formal prerequisite for this book is a one-year course

in calculus, it requires the mathematical sophistication of typical junior and

senior mathematics majors. This book is especially suited for a second course

in linear algebra that emphasizes abstract vector spaces, although it can be

used in a first course with a strong theoretical emphasis.

The book is organized to permit a number of different courses (ranging

from three to eight semester hours in length) to be taught from it. The

core material (vector spaces, linear transformations and matrices, systems of

linear equations, determinants, diagonalization, and inner product spaces) is

found in Chapters 1 through 5 and Sections 6.1 through 6.5. Chapters 6 and

7, on inner product spaces and canonical forms, are completely independent

and may be studied in either order. In addition, throughout the book are

applications to such areas as differential equations, economics, geometry, and

physics. These applications are not central to the mathematical development,

however, and may be excluded at the discretion of the instructor.

We have attempted to make it possible for many of the important topics

of linear algebra to be covered in a one-semester course. This goal has led

us to develop the major topics with fewer preliminaries than in a traditional

approach. (Our treatment of the Jordan canonical form, for instance, does

not require any theory of polynomials.) The resulting economy permits us to

cover the core material of the book (omitting many of the optional sections

and a detailed discussion of determinants) in a one-semester four-hour course

for students who have had some prior exposure to linear algebra.

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# Linear algebra 4th edition

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for courses in advanced linear algebra, this top selling theorem proof text presents a careful treatment of the principal topics of linear algebra and illustrates the power of the subject through a variety of application.it emphasizes the symbiotic relationship between linear transformation and matrices, but states theorems in the more general infinite dimensional case where appropriate.