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Introduction to Matrices and Linear Transformations

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ISBN-10: 048648159X

ISBN-13: 9780486481593

Edition: 3rd 2011

Authors: Daniel T. Finkbeiner

List price: $33.75
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This versatile undergraduate text can be used in a variety of courses in linear algebra. It contains enough material for a one-year course, and it also serves as a support text and reference. A combination of formal theory and related computational techniques, it includes solutions to selected exercises. 1978 edition.
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Book details

List price: $33.75
Edition: 3rd
Copyright year: 2011
Publisher: Dover Publications, Incorporated
Publication date: 6/16/2011
Binding: Paperback
Pages: 480
Size: 5.25" wide x 8.25" long x 0.75" tall
Weight: 1.100
Language: English

Linear Equations
Systems of Linear Equations
Matrix Representation of a Linear System
Solutions of a Linear System
Linear Spaces
Vector Algebra in R<sup>n</sup>
Euclidean n-Space
Vector Spaces
Linear Independence
Bases and Dimension
Isomorphisms of Vector Spaces
Linear Mappings
Algebra of Homomorphisms
Rank and Nullity of a Linear Mapping
Nonsingular Mappings
Matrix Representation of a Linear Mapping
Algebra of Matrices
Special Types of Square Matrices
Elementary Matrices
Rank of a Matrix
Geometry of Linear Systems
Block Multiplication of Matrices
Basic Properties of Determinants
An Explicit Formula for det A
Some Applications of Determinants
Equivalence Relations on Rectangular Matrices
Row Equivalence
Change of Basis
A Canonical form for Similarity
Characteristic Values and Vectors
Invariant Subspaces
The Minimal Polynomial
Nilpotent Transformations
Jordan Canonical Form
Reduction to Jordan Form
An Application of the Hamilton-Cayley Theorem
Inner Product Spaces
Inner Products
Length, Distance, Orthogonality
Scalar-Valued Functions
Linear Functionals
Transpose of a Linear Mapping
Bilinear Functions
Conjunctivity and Congruence
Hermitian and Quadratic Functions
Isometric Diagonability
Application: Linear Programming
Linear Inequalities
Dual Linear Programs
Computational Techniques
Simplex Method
Application: Linear Differential Equations
Sequences and Series of Matrices
Matrix Power Series
Matrices of Functions
Systems of Linear Differential Equations
Appendix A
Algebraic Systems and Fields
Sets and Subsets
Relations and Equivalence Relations
Functions and Operations
Complex Numbers
Solutions for Selected Exercises