Linear Algebra: A Geometric Approach / Edition 1

Linear Algebra: A Geometric Approach / Edition 1

by Ted Shifrin, Malcolm Adams, Theodore Shifrin
     
 

Introducing students to a subject that lies at the foundations of modern mathematics, physics, statistics, and many other disciplines, Linear Algebra: A Geometric Approach appeals to science and engineering students as well as mathematics students making the transition to more abstract advanced courses.  One of the goals of this text is to help

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Overview

Introducing students to a subject that lies at the foundations of modern mathematics, physics, statistics, and many other disciplines, Linear Algebra: A Geometric Approach appeals to science and engineering students as well as mathematics students making the transition to more abstract advanced courses.  One of the goals of this text is to help students learn to think about mathematical concepts and to write rigorous mathematical arguments. The authors do not presuppose any exposure to vectors or vector algebra, and only a passing acquaintance with the derivative and integral is required for certain (optional) topics.
 

Linear Algebra, First Edition is now available exclusively at CourseSmart, as a digital eTextbook.

Product Details

ISBN-13:
9780716743378
Publisher:
Freeman, W. H. & Company
Publication date:
08/28/2001
Edition description:
First Edition
Pages:
464
Product dimensions:
7.16(w) x 9.22(h) x 1.11(d)

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Table of Contents

1. Vectors and Matrices
1. Vectors
2. Dot Product
3. Hyperplanes in Rn
4. Systems of Linear Equations and Gaussian Elimination
5. The Theory of Linear Systems
6. Some Applications

2. Matrix Algebra
1. Matrix Operations
2. Inverse Matrices
3. The Transpose

3. Vector Spaces
1. Subspaces of Rn
2. Linear Independence
3. Basics and Dimension
4. The Four Fundamental Subspaces
5. A Graphic Example
6. Abstract Vector Spaces

4. Projections and Linear Transformations
1. Inconsistent Systems and Projection
2. Orthogonal Bases
3. Linear Transformations
4. Change of Basis

5. Determinants
1. Signed Area in R2
2. Determinants
3. Cofactors and Cramer's Rule

6. Eigenvalues and Eigenvectors
1. The Characteristic Polynomial
2. Diagonalizability
3. Applications
4. Spectral Theorem

7. Further Applications
1. Complex Eigenvalues and Jordan Canonical Form
2. Computer Graphics and Geometry
3. Matrix Exponentials and Differential Equations

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