9780980232714

Introduction to Linear Algebra 4e

by
  • ISBN13:

    9780980232714

  • ISBN10:

    0980232716

  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2/1/2009
  • Publisher: Wellesley Cambridge Pr
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Summary

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
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
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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