Bretscher O. Linear Algebra with Applications

Pearson, 2009. – 504 p. – 4th ed. – ISBN: 0136009263, 0321655621, 9780136009269This trusted reference offers an intellectually honest, thought-provoking, sound introduction to linear algebra. Enables readers to grasp the subject with a challenging, yet visually accessible approach that does not sacrifice mathematical integrity. Adds over 400 new exercises to the problem sets, ranging in difficulty from elementary to more challenging. Adds new historical problems taken from ancient Chinese, Indian, Arabic, and early European sources. Strengthens geometric and conceptual emphasis. A comprehensive, thorough reference for anyone who needs to brush up on their knowledge of linear algebra.Text FeaturesLinear Equations
Introduction to Linear Systems
Matrices, Vectors, and Gauss-Jordan Elimination
On the Solutions of Linear Systems; Matrix Algebra
Linear Transformations
Introduction to Linear Transformations and Their Inverses
Linear Transformations in Geometry
Matrix Products
The Inverse of a Linear Transformation
Subspaces of Mn and Their Dimensions
Image and Kernel of a Linear Transformation
Subspaces of R"; Bases and Linear Independence
The Dimension of a Subspace of R"
Coordinates
Linear Spaces
Introduction to Linear Spaces
Linear Transformations and Isomorphisms
The Matrix of a Linear Transformation
Orthogonality and Least Squares
Orthogonal Projections and Orthonormal Bases
Gram-Schmidt Process and QR Factorization
Orthogonal Transformations and Orthogonal Matrices
Least Squares and Data Fitting
Inner Product Spaces
Determinants
Introduction to Determinants
Properties of the Determinant
Geometrical Interpretations of the Determinant; Cramer’s Rule
Eigenvalues and Eigenvectors
Dynamical Systems and Eigenvectors: An Introductory Example
Finding the Eigenvalues of a Matrix
Finding the Eigenvectors of a Matrix
Diagonalization
Complex Eigenvalues
Stability
Symmetric Matrices and Quadratic Forms
Symmetric Matrices
Quadratic Forms
Singular Values
Linear Differential Equations
An Introduction to Continuous Dynamical Systems
The Complex Case: Euler’s Formula
Linear Differential Operators and
Linear Differential EquationsAppendix A Vectors
Answers to Odd-Numbered Exercises
Subject Index
Name Index