0030105676 BRAND NEW W/FAST SHIPPING! This item is: Linear Algebra and Its Applications, 4th Ed., by Gilbert Strang; FORMAT: Bound Book; ISBN: 9780030105678. Choose Expedited for ...fastest shipping! Our 98%+ rating proves our commitment! We cannot ship to PO Boxes/APO Addresses or outside the continental U.S. To avoid ordering the wrong item, please check your item's ISBN number!Read moreShow Less
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.
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Meet the Author
Gilbert Strang is Professor of Mathematics at the Massachusetts Institute of Technology and an Honorary Fellow of Balliol College. He was an undergraduate at MIT and a Rhodes Scholar at Oxford. His doctorate was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. Professor Strang has published a monograph with George Fix, "An Analysis of the Finite Element Method", and has authored six widely used textbooks. He served as President of SIAM during 1999 and 2000 and he is Chair of the U.S. National Committee on Mathematics for 2003-2004.
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.
I never had a problem solving systems of linear equations, but the advanced concepts never made sense to me. Strang's method of describing vector spaces, eigenvalues and eigenvectors trumps any other text on linear algebra I have read. Examples are useful.
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