(NOTE: A (historic) profile and introduction are keynotes to each chapter.)
1. Linear Systems.
Solving Linear Systems. Echelon Forms, Rank. Applications.
2. Matrices.
Matrix Algebra. Inverses. LU-Factorization. Applications.
3. Vectors.
Spaces of Vectors. Linear Independence, Bases, Dimension. Null Space, Column Space, Row Space. Linear Transformations on Rn.
4. Orthogonality.
Dot Product, Norm. Orthogonal Sets, Orthogonal Matrices. Orthogonal Subspaces, Projections, Bases. Applications.
5. Determinants.
Definition and Computation. Inverses and Products.
6. Eigenvalue Problems.
Eigenvalues and Eigenvectors. Diagonalization. Applied Eignevalue Problems. Markov Chains. Systems of Linear Differential Equations.
7. Vector Spaces.
Vector Spaces and Subspaces. Linear Independence, Basis, Dimension. Coordinates, Linear Transformations.
8. Complex Numbers.
Algebraic Theory. Geometric Theory. Polar Form. Extraction of Roots, Polynomials. Linear Algebra: The Complex Case.
9. Linear Programming.
Standard Forms, Geometrical Methods. The Simplex Algorithm. Duality. Mixed Constraints.
Appendix A: MATLAB.
Appendix B: TOOLBOX.
Answers to Selected Odd-Numbered Exercises
Index.
