Includes bibliographical references and index.

(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.

For a one-semester introductory course. Although the text has been developed in the context of engineering and physical science, it is also suitable for computer science students, math majors, and other quantitative fields. The most carefully written and clearest written text in linear algebra, motivates students in applied areas by placing linear algebra in context through current applications, anecdotes and historical references. Although it may be used without machine computation, the use of MATLAB is encouraged in a unique and innovative way.