Cover image for Linear algebra and matrix theory
Title:
Linear algebra and matrix theory
Personal Author:
Edition:
2nd ed.
Publication Information:
Belmont, CA : Thomson Brooks/Cole, 2004
ISBN:
9780534405816
Added Author:

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30000010235373 QA184 G52 2004 Open Access Book Book
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30000010077167 QA184 G52 2004 Open Access Book
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30000010077166 QA184 G52 2004 Unknown
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Summary

Summary

Master linear algebra with LINEAR ALGEBRA AND MATRIX THEORY! With coverage of the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices, this mathematics text prepares you to succeed in this course and in math courses in your future. Numerous examples and exercises illustrate the theories and provide you with the practice you need to master difficult concepts.


Table of Contents

1 Real Coordinate Spaces
The Vector Spaces Rn
Linear Independence
Subspaces of Rn
Spanning Sets
Geometric Interpretations of R? and R?
Bases and Dimension
2 Elementary Operations On Vectors
Elementary Operations and Their Inverses
Elementary Operations and Linear Independence
Standard Bases for Subspaces
3 Matrix Multiplication
Matrices of Transition
Properties of Matrix Multiplication
Invertible Matrices
Column Operations and Column-Echelon Forms
Row Operations and Row-Echelon Forms
Row and Column Equivalence
Rank and Equivalence
LU Decompositions
4 Vector Spaces, Matrices, and Linear Equations
Vector Spaces
Subspaces and Related Concepts
Isomorphisms of Vector Spaces
Standard Bases for Subspaces
Matrices over an Arbitrary Field
Systems of Linear Equations
More on Systems of Linear Equations
5 Linear Transformations
Linear Transformations
Linear Transformations and Matrices
Change of Basis
Composition of Linear Transformations
6 Determinants
Permutations and Indices
The Definition of a Determinant
Cofactor Expansions
Elementary Operations and Cramer's Rule
Determinants and Matrix Multiplication
7 Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Eigenspaces and Similarity
Representation by a Diagonal Matrix
8 Functions of Vectors
Linear Functionals
Real Quadratic Forms
Orthogonal Matrices
Reduction of Real Quadratic Forms
Classification of Real Quadratic Forms
Binlinear Forms
Symmetric Bilinear Forms
Hermitian Forms
9 Inner Product Spaces
Inner Products
Norms and Distances
Orthonormal Bases
Orthogonal Complements
Isometrics
Normal Matrices
Normal Linear Operators
10 Spectral Decompositions
Projections and Direct Sums
Spectral Decompositions
Minimal Polynomials and Spectral Decompositions
Nilpotent Transformations
The Jordan Canonical Form
11 Numerical Methods
Sequences and Series of Vectors
Sequences and Series of Matrices
The Standard Method of Iteration
Cimmino's Method
An Iterative Method for Determining Eigenvalues