Introduction to Linear Algebra 4e
ISBN: 9780980232714 | 0980232716
Edition: 4thFormat: Hardcover
Publisher: Wellesley Cambridge Pr
Pub. Date: 2/1/2009
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A leading textbook for first courses in linear algebra. Instead of teaching students by repetitive drill, Gilbert Strang encourages students to real mathematical thinking; an approach that has been successful over many years at MIT. The book is supported by online lectures and learning material via http://web.mit.edu/18.06/www/.
This leading textbook for first courses in linear algebra comes from the hugely experienced MIT lecturer and author Gilbert Strang. The book's tried and tested approach is direct, offering ... MORE
This leading textbook for first courses in linear algebra comes from the hugely experienced MIT lecturer and author Gilbert Strang. The book's tried and tested approach is direct, offering ... MORE
| Introduction to Vectors | |
| Vectors and linear combinations | |
| Lengths and dot products | |
| Matrices | |
| Solving Linear Equations | |
| Vectors and linear equations | |
| The idea of elimination | |
| Elimination using matrices | |
| Rules for matrix operations | |
| Inverse matrices | |
| Elimination = factorization: A = LU... MORE | |
| Transposes and permutations | |
| Vector Spaces and Subspaces | |
| Spaces of vectors | |
| The nullspace of A: solving Ax = 0 | |
| The rank and the row reduced form | |
| The complete solution to Ax = b | |
| Independence, basis and dimension | |
| Dimensions of the four subspaces | |
| Orthogonality | |
| Orthogonality of the four subspaces | |
| Projections | |
| Least squares approximations | |
| Orthogonal bases and Gram-Schmidt | |
| Determinants | |
| The properties of determinants | |
| Permutations and cofactors | |
| Cramer's rule, inverses, and Volumes | |
| Eigenvalues and Eigenvectors | |
| Introduction to eigenvalues | |
| Diagonalizing a matrix | |
| Applications to differential equations | |
| Symmetric matrices | |
| Positive definite matrices | |
| Similar matrices | |
| Singular value decomposition (SVD) | |
| Linear Transformations | |
| The idea of a linear transformation | |
| The matrix of a linear transformation | |
| Diagonalization and the pseudoinverse | |
| Applications | |
| Matrices in engineering | |
| Graphs and networks | |
| Markov matrices, population, and economics | |
| Linear programming | |
| Fourier series: linear algebra for functions | |
| Linear algebra for statistics and probability | |
| Computer graphics | |
| Numerical Linear Algebra | |
| Gaussian elimination in practice | |
| Norms and condition numbers | |
| Iterative methods for linear algebra | |
| Complex Vectors and Matrices | |
| Complex numbers | |
| Hermitian and unitary matrices | |
| The fast Fourier transform | |
| Solutions to selected exercises | |
| Matrix factorizations | |
| Conceptual questions for review | |
| Glossary: a dictionary for linear algebra | |
| Index | |
| Teaching codes | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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