《自動控制中的線性代數》是2011年國防工業出版社出版的圖書，作者是author。
基本介紹
- 中文名：自動控制中的線性代數
- 作者：author
- 出版社：國防工業出版社
- 出版時間：2011年12月
- 頁數：348 頁
- 定價：46 元
- ISBN：9787118079012
內容簡介,圖書目錄,
內容簡介
《自動控制中的線性代數》對現行的教材中的每章內容作了簡明扼要的歸納總結；精選的例題力求做到具有典型性、啟發性和針對性。全書共分十章：隨機事件及其機率，隨機變數及其分布，隨機變數的數字特徵，多維隨機變數，大數定理與中心極限定理，數理統計的基本知識，參數估計，假設檢驗，方差分析，回歸分析。
圖書目錄
Chapter 1 Linear Space and Mapping
1.1 Some Basic Concepts of Abstract Algebra
1.1.1 Algebraic Systems
1.1.2 Groups
1.1.3 Rings
1.1.4 Fields
1.2 Linear Spaces
1.2.1 The Basic Concepts
1.2.2 Linear Dependency
1.3 Basis of a Linear Space
1.3.1 The Notion of a Basis
1.3.2 Change of Basis and Transition Matrices
1.4 Linear Subspaces
1.4.1 The Notion of Linear Subspace
1.4.2 Sum and Intersect of Subspaces
1.4.3 Direct Sum and Complementary Subspace
1.5 Linear Transformations
1.5.1 Notion of a Linear Transformation
1.5.2 The Matrix Representation of a Linear Transformation
1.5.3 Isomorphism on Finite Dimensional Linear Spaces
1.5.4 Range and Kernel of a Linear Transformation
1.5.5 Composite Transformation
1.6 Quotient Space
1.6.1 Quotient Space
1.6.2 Regular Projection and Induced Transformation
1.7 Notes and References
1.8 Exercises and Problems
Chapter 2 Polynomials and Matrix Polynomials
2.1 Linear Algebras
2.2 Ring and Euclidean Division
2.3 Ideals of Polynomials
2.4 Factorization of a Polynomial
2.5 Matrix Polynomials
2.6 Unimodular λ-Matrix and the Smith Canonical Form
2.7 Elementary Divisors and Equivalence of Matrix Polynomials
2.8 Ideal of Matrix Polynomials and Coprimeness
2.9 Notes and References
2.10 Problems and Exercises
Chapter 3 Linear Transformations
3.1 The Eigenvalues of a Linear Transformation
3.2 Similarity Reduction, Conditions on Similarity and the NaturalNormal Form
3.2.1 Conditions on Similarity
3.2.2 Similarity Reduction and the Natural Normal Form
3.3 The Jordan Canonical Forms in Cnxn and Rnxn
3.3.1 The Jordan Canonical Forms in Cnxn
3.3.2 The Jordan Canonical Forms in Rnxn
3.3.3 The Transition Matrix X
3.3.4 Decomposing V into the Direct Sum of Jordan Subspaces
3.4 Minimal Polynomials and the First Decomposition of a LinearSpace
3.4.1 Annihilating and Minimal Polynomials
3.4.2 The First Decomposition of a Linear Space
3.4.3 Decomposition of a Linear Space V over the Field C
3.5 The Cyclic Invariant Subspaces and the Second Decomposition ofa Linear Space
3.5.1 The Notion of a Cyclic Invariant Subspace
3.5.2 The Second Decomposition of a Linear Space
3.5.3 Illustrating Examples
3.6 Notes and Reference
3.7 Problems and Exercises
Chapter 4 Linear Transformations in Unitary Spaces
4.1 Euclidean and Unitary Spaces
4.1.1 The Notions of Euclidean and Unitary Spaces
4.1.2 The Characteristics of a Unitary Space
4.1.3 The Metric in Unitary Spaces
4.2 Orthonormal Basis and the Gram-Schmidt Process
4.3 Unitary Transformations
4.4 Projectors and Idempotent Matrices
4.4.1 Projectors and Idempotent Matrices
4.4.2 Orthogonal Complement and Orthogonal Projectors
4.5 Adjoint Transformation
4.6 Normal Transformations and Normal Matrices
4.7 Hermitian Matrices and Hermitian Forms
4.7.1 Hermitian Matrices
4.7.2 Hermitian Forms
4.8 Positive Definite Hermitian Forms
4.9 Canonical Forms of a Hermitian Matrix Pair
4.10 Rayleigh Quotient
4.11 Problems and Exercises
Chapter 5 Decomposition of Linear Transformations andMatrices
5.1 Spectral Decomposition for Simple Linear Transformations andMatrices
5.1.1 Spectral Decomposition of Simple Transformations
5.1.2 Spectral Decomposition of Normal Transformations
5.2 Singular Value Decomposition for Linear Transformations andMatrices
5.3 Full Rank Factorization of Linear Transformations andMatrices
5.4 UR and QR Factorizations of Matrices
5.5 Polar Factorization of Linear Transformations andMatrices
5.6 Problems and Exercises
Chapter 6 Norms for Vectors and Matrices
6.1 Norms for Vectors
6.2 Norms of Matrices
6.3 Induced Norms of Matrices
6.4 Sequences of Matrices and the Convergency
6.5 Power Series of Matrices
6.6 Problems and Exercises
Chapter 7 Functions of Matrices
7.1 Power Series Representation of a Function of Matrices
7.2 Jordan Representation of Functions of Matrices
7.3 Polynomial Representation of a Function of Matrices
7.4 The Lagrange-Sylvester Interpolation Formula
7.5 Exponential and Trigonometric Functions of Matrices
7.5.1 Complex Functions of Matrices
7.5.2 Real Functions of Matrices
7.6 Problems and Exercises
Chapter 8 Matrix-valued Functions and Applications to DifferentialEquations
8.1 Matrix-valued Functions
8.2 Derivative and Integration of Matrix-valued Functions
8.3 Linear Dependency of Vector-valued Functions
8.4 Norms on the Space of Matrix-valued Functions
8.5 The Differential Equation X（t）=A（t）X（t）
8.6 Solution to the State Equation x（t）=Ax（t）+Bu（t）
8.7 Application of the Matrix Exponential Ⅰ: The StabilityTheory
8.8 Application of the Matrix Exponential Ⅱ: Controllability andObservability
8.8.1 Notion on Controllability
8.8.2 Tests for Controllability
8.8.3 Observability and the Tests
8.8.4 Tests for Observability
8.8.5 Essentials of Controllability and Observability
8.8.6 State-Feedback and Stabilization
8.8.7 Observer Design and Output Injection
8.8.8 Co-prime Factorization of a Transfer Function Matrix overH∞
8.8.9 Controllability and Observability Gramian
8.8.10 Balanced Realization
8.9 Application of the Matrix Exponential Ⅲ: The HankelOperator
8.9.1 The Notion of a Hankel Operator
8.9.2 The Singular Values of a Hankel Operator
8.9.3 Schmidt Decomposition of a Hankel Operator
8.10 Notes and References
8.11 Problems and Exercises
Chapter 9 Generalized Inverses of Linear Transformations andMatrices
9.1 The Generalized Inverse of Linear Transformations andMatrices
9.1.1 The Generalized Inverse of Linear Transformations
9.1.2 Generalized Inverses of Matrices
9.2 The Reflexive Generalized Inverse of Linear Transformations andMatrices
9.2.1 The Reflexive Generalized Inverse of LinearTransformations
9.2.2 The Reflexive Generalized Inverse of Matrices
9.3 The Pseudo Inverse of Linear Transformations and Matrices
9.4 Generalized Inverse and Applications to Linear Equations
9.4.1 Consistent Inhomogeneous Linear Equation
9.4.2 Minimum Norm Solution to a Consistent InhomogeneousLinearEquation
9.5 Best Approximation to an Inconsistent Inhomogeneous LinearEquation
9.6 Notes and References
9.7 Problems and Exercises
Chapter 10 Solution to Matrix Equations
10.1 The Notion of Kronecker Product and the Properties
10.2 Eigenvalues and Eigenvectors of Kronecker Product
10.3 Column and Row Expansions of Matrices
10.4 Solution to Linear Matrix Equations
10.5 Solution to Continuous-time Algebraic Riccati Equations
10.6 Solution to Discrete-time Algebraic Riccati Equations
10.7 Discussions and Problems
Bibliography
Notation and Symbols
List of Acronyms
