1. MATRICES AND GAUSSIAN ELIMINATION. 1.1 Introduction. 1.2 The Geometry of Linear Equations. 1.3 An Example of Gaussian Elimination. 1.4 Matrix Notation and Matrix Multiplication. 1.5 Triangular Factors and Row Exchanges. 1.6 Inverses and Transposes. 1.7 Special Matrices and Applications. Review Exercises. 2. VECTOR SPACES. 2.1 Vector Spaces and Subspaces. 2.2 Solving Ax=0 and Ax=b. 2.3 Linear Independence, Basis, and Dimension. 2.4 The Four Fundamental Subspaces. 2.5 Graphs and Networks 2.6 Linear Transformations. Review Exercises. 3. ORTHOGONALITY. 3.1 Orthogonal Vectors and Subspaces. 3.2 Cosines and Projections onto Lines. 3.3 Projections and Linear Squares3.4 Orthogonal Bases and Gram-Schmidt 3.5 The Fast Fourier Transform.�Review Exercises. 4. DETERMINANTS. 4.1 Introduction. 4.2 Properties of the Determinant. 4.3 Formulas for the Determinant. 4.4 Applications of Determinants. Review Exercises. 5. EIGENVALUES AND EIGENVECTORS. 5.1 Introduction. 5.2 Diagonalization of a Matrix. 5.3 Difference Equations and the Powers Ak. 5.4 Differential Equations and� eAt. 5.5 Complex Matrices: 5.6 Similarity Transformations. Review Exercises. 6. POSITIVE DEFINITE MATRICES. 6.1 Minima, Maxima, and Saddle Points. 6.2 Tests for Positive Definiteness. 6.3 Singular Value Decomposition. 6.4 Minimum Principles. 6.5 The Finite Element Method.�7. COMPUTATIONS WITH MATRICES. 7.1 Introduction. 7.2 The Norm and Condition Number. 7.3 Computation of Eigenvalues. 7.4 Iterative Methods for Ax = b. 8. LINEAR PROGRAMMING AND GAME THEORY. 8.1 Linear Inequalities. 8.2 The Simplex Method. 8.3 The Dual Programs. 8.4 Network Models. 8.5 Game Theory. Appendix A: Computer Graphics. Appendix B: The Jordan Form. References. Solutions to Selected Exercises. Matrix FactorizationsGlossaryMATLAB teaching CodesIndex.Linear Algebra in Nutshell