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Introduction to Linear Algebra 4eby Strang, Gilbert
Wellesley Cambridge Pr
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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 practical explanations and examples, while showing the beauty and variety of the subject. Unlike most other linear algebra textbooks, the approach is not a repetitive drill. Instead it inspires an understanding of real mathematics. The book moves gradually and naturally from numbers to vectors to the four fundamental subspaces. This new edition includes challenge problems at the end of each section. Preview five complete sections at math.mit.edu/linearalgebra. Readers can also view freely available online videos of Gilbert Strang's 18.06 linear algebra course at MIT, via OpenCourseWare (ocw.mit.edu), that have been watched by over a million viewers. Also on the web (http://web.mit.edu/18.06/www/), readers will find years of MIT exam questions, MATLAB help files and problem sets to practise what they have learned.
Table of Contents
|Introduction to Vectors|
|Vectors and linear combinations|
|Lengths and dot products|
|Solving Linear Equations|
|Vectors and linear equations|
|The idea of elimination|
|Elimination using matrices|
|Rules for matrix operations|
|Elimination = factorization: A = LU|
|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 of the four subspaces|
|Least squares approximations|
|Orthogonal bases and Gram-Schmidt|
|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|
|Positive definite matrices|
|Singular value decomposition (SVD)|
|The idea of a linear transformation|
|The matrix of a linear transformation|
|Diagonalization and the pseudoinverse|
|Matrices in engineering|
|Graphs and networks|
|Markov matrices, population, and economics|
|Fourier series: linear algebra for functions|
|Linear algebra for statistics and probability|
|Numerical Linear Algebra|
|Gaussian elimination in practice|
|Norms and condition numbers|
|Iterative methods for linear algebra|
|Complex Vectors and Matrices|
|Hermitian and unitary matrices|
|The fast Fourier transform|
|Solutions to selected exercises|
|Conceptual questions for review|
|Glossary: a dictionary for linear algebra|
|Table of Contents provided by Publisher. All Rights Reserved.|