Elementary Linear Algebra

ISBN: 9780120586219 出版年：2003 页码：683 Andrilli, Stephen Hecker, David Academic Press_RM

Vectors and matrices Fundamental operations with vectors The dot product An introduction to proofs Fundamental operations with matrices Matrix multiplication Systems of linear equations Solving systems of linear equations Equivalent systems and rank Row space of a matrix Inverses of matrices Elementary matrices Determinants Introduction to determinants Using row reduction to calculate determinants Finite dimensional vector spaces Subspaces Span Linear independence Basis and dimension Constructing special bases Co-ordinatization Linear transformations and orthogonality Introduction to linear transformations The matrix of a linear transformation The dimension theorem Isomorphism Orthogonality and the Gram-Schmidt process Orthogonal complements Eigenvalues and Eigenvectors Introduction to Eigenvalues Diagonalization Orthogonal diagonalization Complex vector spaces Products Complex vector spaces Inner product spaces Applications Graph theory Ohm's law Least-squares approximations Markov chains Hill substitution: an introduction to coding theory Function spaces Rotation of axes Differential equations Quadratic forms Numerical methods for solving systems LDU decomposition The power method for finding Eigenvalues.