Introduction to linear algebra / by Lee W Johnson; R Dean Riess; Jimmy T Arnold

Index Included

1. Matrices and Systems of Linear Equations.</B> <BR><P></P>Introduction to Matrices and Systems of Linear Equations.<P></P><P></P>Echelon Form and Gauss-Jordan Elimination.<P></P><P></P>Consistent Systems of Linear Equations.<P></P><P></P>Applications (Optional).<P></P><P></P>Matrix Operations.<P></P><P></P>Algebraic Properties of Matrix Operations.<P></P><P></P>Linear Independence and Nonsingular Matrices.<P></P><P></P>Data Fitting, Numerical Integration, and Numerical Differentiation (Optional).<P></P><P></P>Matrix Inverses and Their Properties.<P></P><BR><BR><B>2. Vectors in 2-Space and 3-Space.</B> <BR><P></P>Vectors in the Plane.<P></P><P></P>Vectors in Space.<P></P><P></P>The Dot Product and the Cross Product.<P></P><P></P>Lines and Planes in Space.<P></P><BR><BR><B>3. The Vector Space Rn.</B> <BR><P></P>Introduction.<P></P><P></P>Vector Space Properties of Rn.<P></P><P></P>Examples of Subspaces.<P></P><P></P>Bases for Subspaces.<P></P><P></P>Dimension.<P></P><P></P>Orthogonal Bases for Subspaces.<P></P><P></P>Linear Transformations from Rn to Rm.<P></P><P></P>Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting.<P></P><P></P>Theory and Practice of Least Squares.<P></P><BR><BR><B>4. The Eigenvalue Problem.</B> <BR><P></P>The Eigenvalue Problem for (2 x 2) Matrices.<P></P><P></P>Determinants and the Eigenvalue Problem.<P></P><P></P>Elementary Operations and Determinants (Optional).<P></P><P></P>Eigenvalues and the Characteristic Polynomial.<P></P><P></P>Eigenvectors and Eigenspaces.<P></P><P></P>Complex Eigenvalues and Eigenvectors.<P></P><P></P>Similarity Transformations and Diagonalization.<P></P><P></P>Difference Equations; Markov Chains, Systems of Differential Equations (Optional).<P></P><BR><BR><B>5. Vector Spaces and Linear Transformations.</B> <BR><P></P>Introduction.<P></P><P></P>Vector Spaces.<P></P><P></P>Subspaces.<P></P><P></P>Linear Independence, Bases, and Coordinates.<P></P><P></P>Dimension.<P></P><P></P>Inner-Product Spaces, Orthogonal Bases, and Projections (Optional).<P></P><P></P>Linear Transformations.<P></P><P></P>Operations with Linear Transformations.<P></P><P></P>Matrix Representations for Linear Transformations.<P></P><P></P>Change of Basis and Diagonalization.<P></P><BR><BR><B>6. Determinants.</B> <BR><P></P>Introduction.<P></P><P></P>Cofactor Expansions of Determinants.<P></P><P></P>Elementary Operations and Determinants.<P></P><P></P>Cramer's Rule.<P></P><P></P>Applications of Determinants: Inverses and Wronksians.<P></P><BR><BR><B>7. Eigenvalues and Applications.</B> <BR><P></P>Quadratic Forms.<P></P><P></P>Systems of Differential Equations.<P></P><P></P>Transformation to Hessenberg Form.<P></P><P></P>Eigenvalues of Hessenberg Matrices.<P></P><P></P>Householder Transformations.<P></P><P></P>The QR Factorization and Least-Squares Solutions.<P></P><P></P>Matrix Polynomials and the Cayley-Hamilton Theorem.<P></P><P></P>Generalized Eigenvectors and Solutions of Systems of Differential Equations.<P></P><BR><BR><B>Appendix: An Introduction to MATLAB.</B> <BR><BR><BR><B>Answers to Selected Odd-Numbered Exercises.</B> <BR><BR><BR><B>Index.</B> <BR>