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Generalized vectorization, cross-products, and matrix calculus /
"This book studies the mathematics behind matrix calculus, and the final chapter looks at applications of matrix calculus in statistics and econometrics"--
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2013.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Mathematical prerequisites
- 2. Zero-one matrices
- 3. Elimination and duplication matrices
- 4. Matrix calculus
- 5. New matrix calculus results
- 6. Applications.
- Preface; one Mathematical Prerequisites; 1.1 Introduction; 1.2 Kronecker Products; 1.3 Cross-Product of Matrices; 1.4 Vecs, Rvecs, Generalized Vecs, and Rvecs; 1.4.1 Basic Operators; 1.4.2 Vecs, Rvecs, and the Cross-Product Operator; 1.4.3 Related Operators: Vech and; 1.4.4 Generalized Vecs and Generalized Rvecs; 1.4.5 Generalized Vec Operators and the Cross-Product Operator; two Zero-One Matrices; 2.1 Introduction; 2.2 Selection Matrices and Permutation Matrices; 2.3 The Elementary Matrix; 2.4 The Commutation Matrix; 2.4.1 Commutation Matrices, Kronecker Products, and Vecs.
- 2.4.2 Commutation Matrices and Cross-Products2.5 Generalized Vecs and Rvecs of the Commutation Matrix; 2.5.1 Deriving Results for Generalized Vecs and Rvecs of the Commutation Matrix; 2.5.2 Generalized Vecs and Rvecs of the Commutation Matrix and Cross-Products; 2.5.3; 2.5.4 The Matrix; 2.6 The Matrix; 2.7 Twining Matrices; 2.7.1 Introduction; 2.7.2 Definition and Explicit Expressions for a Twining Matrix; 2.7.3 Twining Matrix and the Commutation Matrix; 2.7.4 Properties of the Twining Matrix .; 2.7.5 Some Special Cases; 2.7.6 Kronecker Products and Twining Matrices; 2.7.7 Generalizations.
- A More General Definition of a Twining Matrix2.7.8 Intertwining Columns of Matrices; Three Elimination and Duplication Matrices; 3.1 Introduction; 3.2 Elimination Matrices; 3.2.1 The Elimination Matrix; 3.2.2 The Elimination Matrix; 3.2.3 The Elimination Matrices and; 3.2.4 The Elimination Matrices; 3.3 Duplication Matrices; 3.3.1 The Duplication Matrix; 3.3.2 The Elimination Matrix and the Duplication Matrix; 3.3.3 The Duplication Matrix; Four Matrix Calculus; 4.1 Introduction; 4.2 Different Concepts of a Derivative of a Matrix with Respect to Another Matrix.
- 4.3 The Commutation Matrix and the Concepts of Matrix Derivatives4.4 Relationships Between the Different Concepts; 4.5 Transformation Principles Between the Concepts; 4.5.1 Concept 1 and Concept 2; 4.5.2 Concept 1 and Concept 3; 4.5.3 Concept 2 and Concept 3; 4.6 Transformation Principle One; 4.7 Transformation Principle Two; 4.8 Recursive Derivatives; Five New Matrix Calculus Results; 5.1 Introduction; 5.2 Concept of a Matrix Derivative Used; 5.3 Some Basic Rules of Matrix Calculus; 5.4 Matrix Calculus Results Involving Generalized Rvecs or Cross-Products.
- 5.5 Matrix Derivatives of Generalized Vecs and Rvecs5.5.1 Introduction; 5.5.2 Large X; Results for Generalized rvecs; Results for Generalized vecs; 5.5.3 Small X; Results for Generalized rvecs; Result for Generalized vecs; 5.6 Matrix Derivatives of Cross-Products; 5.6.1 Basic Cross-Products; 5.6.2 Cross-Products Involving; 5.6.3 Cross-Products Involving; 5.6.4 The Cross-Product; 5.6.5 The Cross-Product; 5.6.6 The Cross-Product; 5.7 Results with Reference to; 5.7.1 Introduction; 5.7.2 Simple Theorems Involving; 5.7.3 Theorems Concerning Derivatives Involving VecA, VechA, and.