Introductory Linear Algebra An Applied First Course

I. INTRODUCTORY LINEAR ALGEBRA. 1. Linear Equations and Matrices. Linear Systems. Matrices. Dot Product and Matrix Multiplication. Properties of Matrix Operations. Graph Theory (Optional). Solutions of Linear Systems of Equations. Electrical Circuits (Optional). Markov Chains (Optional). The Inverse of a Matrix. Linear Economic Models (Optional). Wavelets (Optional). LU-Factorization (Optional). 2. Determinants. Definition and Properties. Cofactor Expansion and Applications. Determinants from a Computational Point of View. 3. Vectors in R2 and R3. Vectors in the Plane. n-Vectors. Introduction to Linear Transformations. Computer Graphics. Computer Graphics (Optional). Cross Products in R 3 (Optional). Lines and Planes. 4. Real Vector Spaces. Real Vector Spaces. Subspaces. Linear Independence. Basis and Dimension. Homogeneous Systems. The Rank of a Matrix and Applications. Coordinates and Change of Basis. Orthonormal Bases in R n. QR-Factorization (Optional). Orthogonal Complements. Least Squares (Optional). 5. Eigenvalues and Eigenvectors. Eigenvalues and Eigenvectors. Diagonalization and Similar Matrices. Diagonalization and Symmetric Matrices. 6. Linear Transformations and Matrices. Definition and Examples. The Kernel and Range of a Linear Transformation. The Matrix of a Linear Transformation. Cumulative Review of Part I. II. OTHER APPLICATIONS. 7. Linear Programming. The Linear Programming Problem; Geometric Solution. The Simplex Method. Duality. The Theory of Games. 8. Applications of Eigenvalues and Eigenvectors. The Fibonacci Sequence. Differential Equations (Calculus Required). Dynamical Systems (Calculus Required). Intro to Fractals. Quadratic Forms. Conic Sections. Quadric Surfaces. Appendix A: Introduction to MATLAB. Appendix B: Complex Numbers. Complex Numbers. Complex Numbers in Linear Algebra. Appendix C: Further Directions. Inner Product Spaces (Calculus Required). Composite and Invertible Linear Transformations. Answers to Odd-Numbered Exercises and Chapter Tests. Index.Kolman, Bernard is the author of 'Introductory Linear Algebra An Applied First Course', published 2001 under ISBN 9780130182654 and ISBN 0130182656.