Advanced Linear Algebra for Engineers with MATLAB

ISBN-10: 1420095234
ISBN-13: 9781420095234
Edition: 2009
List price: $125.95
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Description: Designed to elevate the analytical and problem-solving skills of engineering students, this text provides systematic instruction that will allow those students to make full use of the advanced capacities that MATLAB provides. Based on the applied  More...

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Book details

List price: $125.95
Copyright year: 2009
Publisher: CRC Press LLC
Publication date: 2/23/2009
Binding: Hardcover
Pages: 346
Size: 6.50" wide x 9.75" long x 0.75" tall
Weight: 1.452
Language: English

Designed to elevate the analytical and problem-solving skills of engineering students, this text provides systematic instruction that will allow those students to make full use of the advanced capacities that MATLAB provides. Based on the applied experience of two leading industry consultants in signal and image processing and circuit analysis, this textbook is designed to support the highly regarded courses the two teach at RIT. Offering a broad selection of progressive exercises and MATLAB problems, each chapter features carefully chosen examples that demonstrate underlying ideas at work in practical scenarios. A complete solutions manual is provided for qualifying instructors.

Preface
Authors
Matrices, Matrix Algebra, and Elementary Matrix Operations
Introduction
Basic Concepts and Notation
Matrix and Vector Notation
Matrix Definition
Elementary Matrices
Elementary Matrix Operations
Matrix Algebra
Matrix Addition and Subtraction
Properties of Matrix Addition
Matrix Multiplication
Properties of Matrix Multiplication
Applications of Matrix Multiplication in Signal and Image Processing
Application in Linear Discrete One Dimensional Convolution
Application in Linear Discrete Two Dimensional Convolution
Matrix Representation of Discrete Fourier Transform
Elementary Row Operations
Row Echelon Form
Elementary Transformation Matrices
Type 1: Scaling Transformation Matrix (E<sub>1</sub>
Type 2: Interchange Transformation Matrix (E<sub>2</sub>)
Type 3: Combination Transformation Matrices (E<sub>3</sub>)
Solution of System of Linear Equations
Gaussian Elimination
Over Determined Systems
Under Determined Systems
Matrix Partitions
Column Partitions
Row Partitions
Block Multiplication
Inner, Outer, and Kronecker Products
Inner Product
Outer Product
Kronecker Products
Problems
Determinants, Matrix Inversion and Solutions to Systems of Linear Equations
Introduction
Determinant of a Matrix
Properties of Determinant
Row Operations and Determinants
Interchange of Two Rows
Multiplying a Row of A by a Nonzero Constant
Adding a Multiple of One Row to Another Row
Singular Matrices
Matrix Inversion
Properties of Matrix Inversion
Gauss-Jordan Method for Calculating Inverse of a Matrix
Useful Formulas for Matrix Inversion
Recursive Least Square (RLS) Parameter Estimation
Solution of Simultaneous Linear Equations
Equivalent Systems
Strict Triangular Form
Cramer's Rule
LU Decomposition
Applications: Circuit Analysis
Homogeneous Coordinates System
Applications of Homogeneous Coordinates in Image Processing
Rank, Null Space and Invertibility of Matrices
Null Space N(A)
Column Space C(A)
Row Space R(A)
Rank of a Matrix
Special Matrices with Applications
Vandermonde Matrix
Hankel Matrix
Toeplitz Matrices
Permutation Matrix
Markov Matrices
Circulant Matrices
Hadamard Matrices
Nilpotent Matrices
Derivatives and Gradients
Derivative of Scalar with Respect to a Vector
Quadratic Functions
Derivative of a Vector Function with Respect to a Vector
Problems
Linear Vector Spaces
Introduction
Linear Vector Space
Definition of Linear Vector Space
Examples of Linear Vector Spaces
Additional Properties of Linear Vector Spaces
Subspace of a Linear Vector Space
Span of a Set of Vectors
Spanning Set of a Vector Space
Linear Dependence
Basis Vectors
Change of Basis Vectors
Normed Vector Spaces
Definition of Normed Vector Space
Examples of Normed Vector Spaces
Distance Function
Equivalence of Norms
Inner Product Spaces
Definition of Inner Product
Examples of Inner Product Spaces
Schwarz's Inequality
Norm Derived from Inner Product
Applications of Schwarz Inequality in Communication Systems
Detection of a Discrete Signal �Buried� in White Noise
Detection of Continuous Signal �Buried� in Noise
Hilbert Space
Orthogonality
Orthonormal Set
Gram-Schmidt Orthogonalization Process
Orthogonal Matrices
Complete Orthonormal Set
Generalized Fourier Series (GFS)
Applications of GFS
Continuous Fourier Series
Discrete Fourier Transform (DFT)
Legendre Polynomial
Sinc Functions
Matrix Factorization
QR Factorization
Solution of Linear Equations Using QR Factorization
Problems
Eigenvalues and Eigenvectors
Introduction
Matrices as Linear Transformations
Definition: Linear Transformation
Matrices as Linear Operators
Null Space of a Matrix
Projection Operator
Orthogonal Projection
Projection Theorem
Matrix Representation of Projection Operator
Eigenvalues and Eigenvectors
Definition of Eigenvalues and Eigenvectors
Properties of Eigenvalues and Eigenvectors
Independent Property
Product and Sum of Eigenvalues
Finding the Characteristic Polynomial of a Matrix
Modal Matrix
Matrix Diagonalization
Distinct Eigenvalues
Jordan Canonical Form
Special Matrices
Unitary Matrices
Hermitian Matrices
Definite Matrices
Positive Definite Matrices
Positive Semidefinite Matrices
Negative Definite Matrices
Negative Semidefinite Matrices
Test for Matrix Positiveness
Singular Value Decomposition (SVD)
Definition of SVD
Matrix Norm
Frobenius Norm
Matrix Condition Number
Numerical Computation of Eigenvalues and Eigenvectors
Power Method
Properties of Eigenvalues and Eigenvectors of Different Classes of Matrices
Applications
Image Edge Detection
Gradient Based Edge Detection of Gray Scale Images
Gradient Based Edge Detection of RGB Images
Vibration Analysis
Signal Subspace Decomposition
Frequency Estimation
Direction of Arrival Estimation
Problems
Matrix Polynomials and Functions of Square Matrices
Introduction
Matrix Polynomials
Infinite Series of Matrices
Convergence of an Infinite Matrix Series
Cayley-Hamilton Theorem
Matrix Polynomial Reduction
Functions of Matrices
Sylvester's Expansion
Cayley-Hamilton Technique
Modal Matrix Technique
Special Matrix Functions
Matrix Exponential Function e<sup>At</sup>
Matrix Function A<sup>k</sup>
The State Space Modeling of Linear Continuous-time Systems
Concept of States
State Equations of Continuous Time Systems
State Space Representation of Continuous LTI Systems
Solution of Continuous-time State Space Equations
Solution of Homogenous State Equations and State Transition Matrix
Properties of State Transition Matrix
Computing State Transition Matrix
Complete Solution of State Equations
State Space Representation of Discrete-time Systems
Definition of States
State Equations
State Space Representation of Discrete-time LTI Systems
Solution of Discrete-time State Equations
Solution of Homogenous State Equation and State Transition Matrix
Properties of State Transition Matrix
Computing the State Transition Matrix
Complete Solution of the State Equations
Controllability of LTI Systems
Definition of Controllability
Controllability Condition
Observability of LTI Systems
Definition of Observability
Observability Condition
Problems
Introduction to Optimization
Introduction
Stationary Points of Functions of Several Variables
Hessian Matrix
Least-Square (LS) Technique
LS Computation Using QR Factorization
LS Computation Using Singtilar Value Decomposition (SVD)
Weighted Least Square (WLS)
LS Curve Fitting
Applications of LS Technique
One Dimensional Wiener Filter
Choice of Q Matrix and Scale Factor �
Two Dimensional Wiener Filter
Total Least-Squares (TLS)
Eigen Filters
Stationary Points with Equality Constraints
Lagrange Multipliers
Applications
Maximum Entropy Problem
Design of Digital Finite Impulse Response (FIR) Filters
Problems
The Laplace Transform
Definition of the Laplace Transform
The Inverse Laplace Transform
Partial Fraction Expansion
The z-Transform
Definition of the z-Transform
The Inverse z-Transform
Inversion by Partial Fraction Expansion
Bibliography
Index

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