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1.

図書
図書
1. Matrix differential calculus with applications in statistics and econometrics
Jan R. Magnus and Heinz Neudecker
出版情報: Chichester [West Sussex] ; New York : Wiley, c1988  xvii, 393 p. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics ; . Applied probability and statistics
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Matrices
Basic Properties of Vectors and Matrices
Kronecker Products, the Vec-Operator, and the Moore-Penrose Inverse
Miscellaneous Matrix Results
Differentials: The Theory
Mathematical Preliminaries
Differentials and Differentiability
The Second Differential
Static Optimization
Differentials: The Practice
Some Important Differentials
First-Order Differentials and Jacobian Matrices
Second-Order Differentials and Hessian Matrices
Inequalities
The Linear Model
Statistical Preliminaries
The Linear Regression Model
Further Topics in the Linear Model
Applications To Maximum Likelihood Estimation
Maximum Likelihood Estimation
Simultaneous Equations
Topics in Psychometrics
Index
Matrices
Basic Properties of Vectors and Matrices
Kronecker Products, the Vec-Operator, and the Moore-Penrose Inverse
2.

図書
図書
2. Matrix differential calculus with applications in statistics and econometrics. Rev. ed (: hbk ; : pbk)
Jan R. Magnus and Heinz Neudecker
出版情報: Chichester ; New York : Wiley, c1999  xviii, 395 p. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics ; . Applied probability and statistics
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Matrices: Basic Properties of Vectors and Matrices
Kronecker Products, the Vec Operator and the Moore-Penrose Inverse
Miscellaneous Matrix Results
Differentials: The Theory: Mathematical Preliminaries
Differentials and Differentiability
The Second Differential
Static Optimization
Differentials: The Practice: Some Important Differentials
First Order Differentials and Jacobian Matrices
Second Order Differentials and Hessian Matrices
Inequalities: Inequalities
The Linear Model: Statistical Preliminaries
The Linear Regression Model
Further Topics in the Linear Model
Applications to Maximum Likelihood Estimation: Maximum Likelihood Estimation
Simultaneous Equations
Topics in Psychometrics
Matrices: Basic Properties of Vectors and Matrices
Kronecker Products, the Vec Operator and the Moore-Penrose Inverse
Miscellaneous Matrix Results
3.

図書
図書
3. Matrix algebra (: pbk)
Karim M. Abadir, Jan R. Magnus
出版情報: Cambridge ; New York : Cambridge University Press, 2005  xxx, 434 p. ; 25-26 cm
シリーズ名: Econometric exercises ; 1
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List of exercises
Preface to the series
Preface
Vectors / 1：
Real vectors / 1.1：
Complex vectors / 1.2：
Matrices / 2：
Real matrices / 2.1：
Complex matrices / 2.2：
Vector spaces / 3：
Complex and real vector spaces / 3.1：
Inner-product space / 3.2：
Hilbert space / 3.3：
Rank, inverse, and determinant / 4：
Rank / 4.1：
Inverse / 4.2：
Determinant / 4.3：
Partitioned matrices / 5：
Basic results and multiplication relations / 5.1：
Inverses / 5.2：
Determinants / 5.3：
Rank (in)equalities / 5.4：
The sweep operator / 5.5：
Systems of equations / 6：
Elementary matrices / 6.1：
Echelon matrices / 6.2：
Gaussian elimination / 6.3：
Homogeneous equations / 6.4：
Nonhomogeneous equations / 6.5：
Eigenvalues, eigenvectors, and factorizations / 7：
Eigenvalues and eigenvectors / 7.1：
Symmetric matrices / 7.2：
Some results for triangular matrices / 7.3：
Schur's decomposition theorem and its consequences / 7.4：
Jordan's decomposition theorem / 7.5：
Jordan chains and generalized eigenvectors / 7.6：
Positive (semi)definite and idempotent matrices / 8：
Positive (semi)definite matrices / 8.1：
Partitioning and positive (semi)definite matrices / 8.2：
Idempotent matrices / 8.3：
Matrix functions / 9：
Simple functions / 9.1：
Jordan representation / 9.2：
Matrix-polynomial representation / 9.3：
Kronecker product, vec-operator, and Moore-Penrose inverse / 10：
The Kronecker product / 10.1：
The vec-operator / 10.2：
The Moore-Penrose inverse / 10.3：
Linear vector and matrix equations / 10.4：
The generalized inverse / 10.5：
Patterned matrices: commutation- and duplication matrix / 11：
The commutation matrix / 11.1：
The symmetrizer matrix / 11.2：
The vech-operator and the duplication matrix / 11.3：
Linear structures / 11.4：
Matrix inequalities / 12：
Cauchy-Schwarz type inequalities / 12.1：
Positive (semi)definite matrix inequalities / 12.2：
Inequalities derived from the Schur complement / 12.3：
Inequalities concerning eigenvalues / 12.4：
Matrix calculus / 13：
Basic properties of differentials / 13.1：
Scalar functions / 13.2：
Vector functions / 13.3：
The inverse / 13.4：
Exponential and logarithm / 13.6：
The determinant / 13.7：
Jacobians / 13.8：
Sensitivity analysis in regression models / 13.9：
The Hessian matrix / 13.10：
Least squares and best linear unbiased estimation / 13.11：
Maximum likelihood estimation / 13.12：
Inequalities and equalities / 13.13：
Some mathematical tools / Appendix A：
Some methods of indirect proof / A.1：
Primer on complex numbers and polynomials / A.2：
Series expansions / A.3：
Sequences and limits / A.3.1：
Convergence of series / A.3.2：
Special series / A.3.3：
Expansions of functions / A.3.4：
Multiple series, products, and their relation / A.3.5：
Further calculus / A.4：
Linear difference equations / A.4.1：
Convexity / A.4.2：
Constrained optimization / A.4.3：
Notation / Appendix B：
Vectors and matrices / B.1：
Mathematical symbols, functions, and operators / B.2：
Bibliography
List of exercises
Preface to the series
Preface
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