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Matrix Algebra

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ISBN-10: 0521537460

ISBN-13: 9780521537469

Edition: 2005

Authors: Karim M. Abadir, Jan R. Magnus, Jan Magnus, Jan Magnus, Peter C. B. Phillips

List price: $69.99
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Description:

The first volume of the Econometric Exercises Series, Matrix Algebra contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undegraduate or a postgraduate course in econometrics or statistics. The book features a comprehensive collection of exercises with complete answers. More than just a collection of exercises, the volume is a textbook organized in a completely different manner than the usual textbook. It can be used as a self-contained course in matrix algebra or as a supplementary text.
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Book details

List price: $69.99
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 8/22/2005
Binding: Paperback
Pages: 466
Size: 6.69" wide x 9.61" long x 0.94" tall
Weight: 1.936
Language: English

Karim Abadir has held a joint Chair since 1996 in the Department of Mathematics and Economics at the University of York, where he has been the founder and director of various degree programs. He has also taught at the American University in Cairo, the University of Oxford, and the University of Exeter. He became an Extramural Fellow at CentER (Tilburg University) in 1993. Professor Abadir is a holder of two Econometric Theory awards, and has authored many articles in top journals, including the Annals of Statistics, Econometric Theory, Econometrica, and the Journal of Physics. He is Coordinating Editor (and one of the founding editors) of the Econometrics Journal, and Associate Editor of…    

List of exercises
Preface to the series
Preface
Vectors
Real vectors
Complex vectors
Matrices
Real matrices
Complex matrices
Vector spaces
Complex and real vector spaces
Inner-product space
Hilbert space
Rank, inverse, and determinant
Rank
Inverse
Determinant
Partitioned matrices
Basic results and multiplication relations
Inverses
Determinants
Rank (in)equalities
The sweep operator
Systems of equations
Elementary matrices
Echelon matrices
Gaussian elimination
Homogeneous equations
Nonhomogeneous equations
Eigenvalues, eigenvectors, and factorizations
Eigenvalues and eigenvectors
Symmetric matrices
Some results for triangular matrices
Schur's decomposition theorem and its consequences
Jordan's decomposition theorem
Jordan chains and generalized eigenvectors
Positive (semi)definite and idempotent matrices
Positive (semi)definite matrices
Partitioning and positive (semi)definite matrices
Idempotent matrices
Matrix functions
Simple functions
Jordan representation
Matrix-polynomial representation
Kronecker product, vec-operator, and Moore-Penrose inverse
The Kronecker product
The vec-operator
The Moore-Penrose inverse
Linear vector and matrix equations
The generalized inverse
Patterned matrices: commutation- and duplication matrix
The commutation matrix
The symmetrizer matrix
The vech-operator and the duplication matrix
Linear structures
Matrix inequalities
Cauchy-Schwarz type inequalities
Positive (semi)definite matrix inequalities
Inequalities derived from the Schur complement
Inequalities concerning eigenvalues
Matrix calculus
Basic properties of differentials
Scalar functions
Vector functions
Matrix functions
The inverse
Exponential and logarithm
The determinant
Jacobians
Sensitivity analysis in regression models
The Hessian matrix
Least squares and best linear unbiased estimation
Maximum likelihood estimation
Inequalities and equalities
Some mathematical tools
Some methods of indirect proof
Primer on complex numbers and polynomials
Series expansions
Sequences and limits
Convergence of series
Special series
Expansions of functions
Multiple series, products, and their relation
Further calculus
Linear difference equations
Convexity
Constrained optimization
Notation
Vectors and matrices
Mathematical symbols, functions, and operators
Bibliography