Matrix Analysis for Scientists and Engineers

ISBN-10: 0898715768
ISBN-13: 9780898715767
Edition: 2005
Authors: Alan J. Laub
List price: $36.00
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Description: Matrix Analysis for Scientists and Engineers provides a blend of undergraduate- and graduate-level topics in matrix theory and linear algebra that relieves instructors of the burden of reviewing such material in subsequent courses that depend  More...

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Book details

List price: $36.00
Copyright year: 2005
Publisher: Society for Industrial and Applied Mathematics
Binding: Paperback
Pages: 184
Size: 7.00" wide x 10.00" long x 0.50" tall
Weight: 1.056
Language: English

Matrix Analysis for Scientists and Engineers provides a blend of undergraduate- and graduate-level topics in matrix theory and linear algebra that relieves instructors of the burden of reviewing such material in subsequent courses that depend heavily on the language of matrices. Consequently, the text provides an often-needed bridge between undergraduate-level matrix theory and linear algebra and the level of matrix analysis required for graduate-level study and research. The text is sufficiently compact that the material can be taught comfortably in a one-quarter or one-semester course. Throughout the book, the author emphasizes the concept of matrix factorization to provide a foundation for a later course in numerical linear algebra. The author addresses connections to differential and difference equations as well as to linear system theory and encourages instructors to augment these examples with other applications of their own choosing.

Preface
Introduction and Review
Some Notation and Terminology
Matrix Arithmetic
Inner Products and Orthogonality
Determinants
Vector Spaces
Definitions and Examples
Subspaces
Linear Independence
Sums and Intersections of Subspaces
Linear Transformations
Definition and Examples
Matrix Representation of Linear Transformations
Composition of Transformations
Structure of Linear Transformations
Four Fundamental Subspaces
Introduction to the Moore-Penrose Pseudoinverse
Definitions and Characterizations
Examples
Properties and Applications
Introduction to the Singular Value Decomposition
The Fundamental Theorem
Some Basic Properties
Row and Column Compressions
Linear Equations
Vector Linear Equations
Matrix Linear Equations
A More General Matrix Linear Equation
Some Useful and Interesting Inverses
Projections, Inner Product Spaces, and Norms
Projections
The four fundamental orthogonal projections
Inner Product Spaces
Vector Norms
Matrix Norms
Linear Least Squares Problems
The Linear Least Squares Problem
Geometric Solution
Linear Regression and Other Linear Least Squares Problems
Example: Linear regression
Other least squares problems
Least Squares and Singular Value Decomposition
Least Squares and QR Factorization
Eigenvalues and Eigenvectors
Fundamental Definitions and Properties
Jordan Canonical Form
Determination of the JCF
Theoretical computation
On the +1's in JCF blocks
Geometric Aspects of the JCF
The Matrix Sign Function
Canonical Forms
Some Basic Canonical Forms
Definite Matrices
Equivalence Transformations and Congruence
Block matrices and definiteness
Rational Canonical Form
Linear Differential and Difference Equations
Differential Equations
Properties of the matrix exponential
Homogeneous linear differential equations
Inhomogeneous linear differential equations
Linear matrix differential equations
Modal decompositions
Computation of the matrix exponential
Difference Equations
Homogeneous linear difference equations
Inhomogeneous linear difference equations
Computation of matrix powers
Higher-Order Equations
Generalized Eigenvalue Problems
The Generalized Eigenvalue/Eigenvector Problem
Canonical Forms
Application to the Computation of System Zeros
Symmetric Generalized Eigenvalue Problems
Simultaneous Diagonalization
Simultaneous diagonalization via SVD
Higher-Order Eigenvalue Problems
Conversion to first-order form
Kronecker Products
Definition and Examples
Properties of the Kronecker Product
Application to Sylvester and Lyapunov Equations
Bibliography
Index

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