Elementary Linear Algebra

✍ Scribed by Ron Larson

• Publisher: Cengage Learning
• Year: 2012
• Tongue: English
• Leaves: 635
• Edition: 7th edition (January 1, 2012)
• Category: Library

✦ Synopsis

Designed specifically for the introductory course, this text' s uniquely motivating approach helps math or science and engineering majors truly understand how linear algebra works. Balancing theory with examples, applications, and geometrical interpretation, "Elementary Linear Algebra also includes opportunities to incorporate technology.In response to users' requests, the Fourth Edition has been streamlined to seven chapters, with material from previous chapters 8-10 (Complex Vector Spaces, Linear Programming, and Numerical Methods) now available on the accompanying web site. In addition, all MATLAB exercises have been moved from the text to the web site.

✦ 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. --This text refers to an out of print or unavailable edition of this title.