Linear Algebra And Its Application

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

Salient Features

• 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.

Table Of Contents

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