Elementary Linear Algebra / Edition 7

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Overview

The cornerstone of ELEMENTARY LINEAR ALGEBRA is the authors' clear, careful, and concise presentation of material—written so that readers can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. Featuring a new design that highlights the relevance of the mathematics and improves readability, the Seventh Edition also incorporates new conceptual Capstone exercises that reinforce multiple concepts in each section. Data and applications reflect current statistics and examples to engage users and demonstrate the link between theory and practice.

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Product Details

  • ISBN-13: 9781133110873
  • Publisher: Cengage Learning
  • Publication date: 1/1/2012
  • Edition description: New Edition
  • Edition number: 7
  • Pages: 448
  • Sales rank: 155,155
  • Product dimensions: 8.70 (w) x 11.00 (h) x 0.80 (d)

Meet the Author

Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, the 2011 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning.

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Table of Contents

1. SYSTEMS OF LINEAR EQUATIONS Introduction to Systems of Equations. Gaussian Elimination and Gauss-Jordan Elimination. Applications of Systems of Linear Equations. 2. MATRICES. Operations with Matrices. Properties of Matrix Operations. The Inverse of a Matrix. Elementary Matrices. Applications of Matrix Operations. 3. DETERMINANTS. The Determinant of a Matrix. Evaluation of a Determinant Using Elementary Operations. Properties of Determinants. Applications of Determinants. 4. VECTOR SPACES. Vectors in Rn. Vector Spaces. Subspaces of Vector Spaces. Spanning Sets and Linear Independence. Basis and Dimension. Rank of a Matrix and Systems of Linear Equations. Coordinates and Change of Basis. Applications of Vector Spaces. 5. INNER PRODUCT SPACES. Length and Dot Product in Rn. Inner Product Spaces. Orthogonal Bases: Gram-Schmidt Process. Mathematical Models and Least Squares Analysis. Applications of Inner Product Spaces. 6. LINEAR TRANSFORMATIONS. Introduction to Linear Transformations. The Kernel and Range of a Linear Transformation. Matrices for Linear Transformations. Transition Matrices and Similarity. Applications of Linear Transformations. 7. EIGENVALUES AND EIGENVECTORS. Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices and Orthogonal Diagonalization. Applications of Eigenvalues and Eigenvectors. 8. COMPLEX VECTOR SPACES (online). Complex Numbers. Conjugates and Division of Complex Numbers. Polar Form and Demoivre's Theorem. Complex Vector Spaces and Inner Products. Unitary and Hermitian Spaces. 9. LINEAR PROGRAMMING (online). Systems of Linear Inequalities. Linear Programming Involving Two Variables. The Simplex Method: Maximization. The Simplex Method: Minimization. The Simplex Method: Mixed Constraints. 10. NUMERICAL METHODS (online). Gaussian Elimination with Partial Pivoting. Iterative Methods for Solving Linear Systems. Power Method for Approximating Eigenvalues. Applications of Numerical Methods.

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