Introduction to linear algebra

Book Description: Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, Fourier methods and the FFT, linear programming, and computer graphics. Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.

Includes index.

1: Introduction To Vectors: -- 1-1: Vectors and linear combinations -- 1-2: Lengths and dot products -- 1-3: Matrices -- 2: Solving Linear Equations: -- 2-1: Vectors and linear equations -- 2-2: Idea of elimination -- 2-3: Elimination using matrices -- 2-4: Rules for matrix operations -- 2-5: Inverse matrices -- 2-6: Elimination = factorization: A = LU -- 2-7: Transposes and permutations -- 3: Vector Spaces And Subspaces: -- 3-1: Spaces of vectors -- 3-2: Nullspace of A: Solving Ax = 0 -- 3-3: Rank and the row reduced form -- 3-4: Complete solution to Ax = b -- 3-5: Independence, basis and dimension -- 3-6: Dimensions of the four subspaces -- 4: Orthogonality: -- 4-1: Orthogonality of the four subspaces -- 4-2: Projections -- 4-3: Least squares approximations -- 4-4: Orthogonal bases and gram-Schmidt -- 5: Determinants -- 5-1: Properties of determinants -- 5-2: Permutations and cofactors -- 5-3: Cramer's rule, inverses, and volumes -- 6: Eigenvalues And Eigenvectors: -- 6-1: Introduction to eigenvalues -- 6-2: Diagonalizing a matrix -- 6-3: Applications to differential equations -- 6-4: Symmetric matrices -- 6-5: Positive definite matrices -- 6-6: Similar matrices -- 6-7: Singular…