Linear Algebra And Its Applications 3e

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete R n setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts are more accessible.


Features



MyMathLab

Interactive Content-The full text is now available online, integrating the text's content with the Student's Study Guide and electronic practice problems. All of the text's many electronic resources can be found on MyMathLab.

Fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of R n, and then gradually examined from different points of view. Later generalizations of these concepts appear as natural extensions of familiar ideas.

Focus on visualization of concepts throughout the book.

Icons in the margins to flag topics for which expanded or enhanced material is available on the Web.

A modern view of matrix multiplication is presented. Definitions and proofs focus on the columns of a matrix rather than on the matrix entries.

Numerical Notes give a realistic flavor to the text. Students are reminded frequently of issues that arise in the real-life use of linear algebra.

Each major concept in the course is given a geometric interpretation because many students learn better when they can visualize an idea.

M exercises appear in every section.

NEW-New full color design allows for clearer understanding of figures and graphically important concepts and procedures.

NEW-Section 1.6, Applications of Linear Systems, is new to this edition. It includes applications on the Leontief Economic Model, Solving Chemical Equations, and Traffic Flow.

NEW-Section 2.9 from the Updated 2/e, Subspaces of R n, has been split into two sections, 2.8 and 2.9. This forms a better bridge to Chapter 5 for those instructors who wish to cover Eigenvalues earlier in the course, or postpone or omit vector spaces. This option is ideal for a shorter course.
NEW-MyMathLab is now available, integrating the text's content with the Student Study Guide. All of the text's many electronic resources can be found on MyMathLab.
NEW-MathXL is now available for the text, allowing students to take tests and quizzes online.
NEW-An electronic test generator, TestGen-EQ, allows for creation of paper tests, or can be used in conjunction with MathXL to test or do homework online.

Contents
Linear Equations in Linear Algebra.
Matrix Algebra.
Determinants.
Vector Spaces.
Eigenvalues and Eigenvectors.
Orthogonality and Least-Squares.
Symmetric Matrices and Quadratic Forms.

About the Author
David C. Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has also served as a visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of Kaiserslautern, Germany. He has over 30 research articles published in functional analysis and linear algebra.