Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.
"synopsis" may belong to another edition of this title.
1. MATRICES AND GAUSSIAN ELIMINATION. Introduction. The Geometry of Linear Equations. An Example of Gaussian Elimination. Matrix Notation and Matrix Multiplication. Triangular Factors and Row Exchanges. Inverses and Transposes. Special Matrices and Applications. Review Exercises. 2. VECTOR SPACES. Vector Spaces and Subspaces. The Solution of m Equations in n Unknowns. Linear Independence, Basis, and Dimension. The Four Fundamental Subspaces. Networks and Incidence Matrices. Linear Transformations. Review Exercises. 3. ORTHOGONALITY. Perpendicular Vectors and Orthogonal Subspaces. Inner Products and Projections onto Lines. Least Squares Approximations. Orthogonal Bases, Orthogonal Matrices, and Gram-Schmidt Orthogonalization. The Fast Fourier Transform. Review and Preview. Review Exercises. 4. DETERMINANTS. Introduction. Properties of the Determinant. Formulas for the Determinant. Applications of Determinants. Review Exercises. 5. EIGENVALUES AND EIGENVECTORS. Introduction. Diagonalization of a Matrix. Difference Equations and the Powers Ak. Differential Equations and the Exponential eAt. Complex Matrices: Symmetric vs. Hermitian. Similarity Transformations. Review Exercises. 6. POSITIVE DEFINITE MATRICES. Minima, Maxima, and Saddle Points. Tests for Positive Definiteness. The Singular Value Decomposition. Minimum Principles. The Finite Element Method. 7. COMPUTATIONS WITH MATRICES. Introduction. The Norm and Condition Number. The Computation of Eigenvalues. Iterative Methods for Ax = b. 8. LINEAR PROGRAMMING AND GAME THEORY. Linear Inequalities. The Simplex Method. Primal and Dual Programs. Network Models. Game Theory. Appendix A: Computer Graphics. Appendix B: The Jordan Form. References. Solutions to Selected Exercises. Index.
"About this title" may belong to another edition of this title.
Book Description Academic Press Inc, 1980. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service!. Bookseller Inventory # ABE_book_new_012673660X
Book Description Academic Press Inc, 1980. Hardcover. Book Condition: New. book. Bookseller Inventory # 012673660X
Book Description Academic Press Inc, 1980. Hardcover. Book Condition: New. 2nd. Bookseller Inventory # DADAX012673660X
Book Description Academic Press Inc. Hardcover. Book Condition: New. 012673660X New. Has the slightest of shelf wear (like you might see in a major bookstore chain). Looks like an interesting title! We provide domestic tracking upon request, provide personalized customer service and want you to have a great experience purchasing from us. 100% satisfaction guaranteed and thank you for your consideration. Bookseller Inventory # E-012673660X
Book Description Academic Press Inc, 1980. Hardcover. Book Condition: New. Bookseller Inventory # P11012673660X