[request_ebook] Contemporary Linear Algebra

Description

Contents
(Click on the Section Number for a List of Topics in the Section)

Chapter 1  Vectors
Section 1.1 — Vectors and Matrices in Engineering and Mathematics; n-space
Section 1.2 — Dot Product and Orthogonality
Section 1.3 — Vector Equations of Lines and Planes

Chapter 2  Systems of Linear Equations
Section 2.1 — Introduction to Systems of Linear Equations
Section 2.2 — Solving Linear Systems by Row Reduction
Section 2.3 — Applications of Linear Systems

Chapter 3  Matrices and Matrix Algebra
Section 3.1 — Operations on Matrices
Section 3.2 — Inverses; Algebraic Properties of Matrices
Section 3.3 — Elementary Matrices; A Method for Finding the Inverse of a Matrix
Section 3.4 — Subspaces and Linear Independence
Section 3.5 — The Geometry of Linear Systems
Section 3.6 — Matrices with Special Forms
Section 3.7 — Matrix Factorizations; LU-Decomposition
Section 3.8 — Partitioned Matrices and Parallel Processing

Chapter 4  Determinants
Section 4.1 — Determinants; Cofactor Expansion
Section 4.2 — Properties of Determinants
Section 4.3 — Cramer's Rule; Formula for the Inverse of a Matrix; Applications of Determinants
Section 4.4 — A First Look at Eigenvalues and Eigenvectors

Chapter 5  Matrix Models
Section 5.1 — Dynamical Systems and Markov Chains
Section 5.2 — Leontief Input-Output Models
Section 5.3 — Gauss-Seidel and Jacobi Iteration; Sparse Linear Systems
Section 5.4 — The Power Method; Application to Internet Search Engines

Chapter 6   Linear Transformations
Section 6.1 — Matrices as Transformations
Section 6.2 — Geometry of Linear Operators
Section 6.3 — Kernel and Range
Section 6.4 — Composition and Invertibility of Linear Transformations
Section 6.5 — Computer Graphics

Chapter 7   Dimension and Structure
Section 7.1 — Basis and Dimension
Section 7.2 — Properties of Bases
Section 7.3 — The Fundamental Spaces of a Matrix
Section 7.4 — The Dimension Theorem and Its Implications
Section 7.5 — The Rank Theorem and Its Implications
Section 7.6 — The Pivot Theorem and Its Implications
Section 7.7 — The Projection Theorem and Its Implications
Section 7.8 — Best Approximation and Least Squares
Section 7.9 — Orthonormal Bases and the Gram-Schmidt Process
Section 7.10 — QR-Decomposition; Householder Transformations
Section 7.11 — Coordinates with Respect to a Basis

Chapter 8   Diagonalization
Section 8.1 — Matrix Representations of Linear Transformations
Section 8.2 — Similarity and Diagonalizability
Section 8.3 — Orthogonal Diagonalizability; Functions of a Matrix
Section 8.4 — Quadratic Forms
Section 8.5 — Application of Quadratic Forms to Optimization
Section 8.6 — Singular Value Decomposition
Section 8.7 — The Pseudoinverse
Section 8.8 — Complex Eigenvalues and Eigenvectors
Section 8.9 — Hermitian, Unitary, and Normal Matrices
Section 8.10 — Systems of Differential Equations

CHAPTER 9   General Vector Spaces
Section 9.1 — Vector Space Axioms
Section 9.2 — Inner Product Spaces; Fourier Series
Section 9.3 — General Linear Transformations; Isomorphism

Appendix A  How to Read Theorems

Appendix B  Complex Numbers

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