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Matrix Algebra

$50.00 USD

Part of Econometric Exercises

  • Date Published: December 2007
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511343179

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About the Authors
  • Matrix Algebra is the first volume of the Econometric Exercises Series. It contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undergraduate or a postgraduate course in econometrics or statistics. The book contains a comprehensive collection of exercises, all with full answers. But the book is not just a collection of exercises; in fact, it is a textbook, though one that is organized in a completely different manner than the usual textbook. The volume can be used either as a self-contained course in matrix algebra or as a supplementary text.

    • Only text that is devoted to solved examples in matrix algebra
    • Nearly 400 pages of solved problems
    • Can be used either as a self-contained course in matrix algebra or as a supplementary text
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    Reviews & endorsements

    'These authors have achieved the remarkable feat of writing a textbook of matrix algebra cunningly concealed as a structured sequence of exercises and worked answers. The book should prove popular with students intent on teaching themselves and with instructors who wish to set challenging and educative exercises. Recommended unequivocally to all parties.' Dr Stephen Pollock, Queen Mary College

    'Useful as a text or reference, it is clearly written and very thorough. Besides basic topics, excellent treatment of matrix inequalities, vectorization, and matrix calculus. It belongs on every econometricians's bookshelf.' Professor Peter Schmidt, Michigan State University

    'Matrix Algebra can be recommended to teachers and graduate students in all fields of mathematics.' Zentralblatt MATH

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    Product details

    • Date Published: December 2007
    • format: Adobe eBook Reader
    • isbn: 9780511343179
    • contains: 9 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Part I. Vectors:
    1. Real vectors
    2 Complex vectors
    Part II. Matrices:
    3. Real matrices
    4. Complex matrices
    Part III. Vector Spaces:
    5. Complex and real vector spaces
    6. Inner-product space
    7. Hilbert space
    Part IV. Rank, Inverse, and Determinant:
    8. Rank
    9. Inverse
    10. Determinant
    Part V. Partitioned Matrices:
    11. Basic results and multiplication relations
    12. Inverses
    13. Determinants
    14. Rank (in)equalities
    15. The sweep operator
    Part VI. Systems of Equations:
    16. Elementary matrices
    17. Echelon matrices
    18. Gaussian elimination
    19. Homogeneous equations
    20. Nonhomogeneous equations
    Part VII. Eigenvalues, Eigenvectors, and Factorizations:
    21. Eigenvalues and eigenvectors
    22. Symmetric matrices
    23. Some results for triangular matrices
    24. Schur's decomposition theorem and its consequences
    25. Jordan's decomposition theorem
    26. Jordan chains and generalized eigenvectors
    Part VIII. Positive (Semi)Definite and Idempotent Matrices:
    27. Positive (semi)definite matrices
    28. Partitioning and positive (semi)definite matrices
    29. Idempotent matrices
    Part IX. Matrix Functions:
    30. Simple functions
    31. Jordan representation
    32. Matrix-polynomial representation
    Part X. Kronecker Product, Vec-Operator, and Moore-Penrose Inverse:
    33. The Kronecker product
    34. The vec-operator
    35. The Moore-Penrose inverse
    36. Linear vector and matrix equations
    37. The generalized inverse
    Part XI. Patterned Matrices, Commutation and Duplication Matrix:
    38. The commutation matrix
    39. The symmetrizer matrix
    40. The vec-operator and the duplication matrix
    41. Linear structures
    Part XII. Matrix Inequalities:
    42. Cauchy-Schwarz type inequalities
    43. Positive (semi)definite matrix inequalities
    44. Inequalities derived from the Schur complement
    45. Inequalities concerning eigenvalues
    Part XIII. Matrix calculus:
    46. Basic properties of differentials
    47. Scalar functions
    48. Vector functions
    49. Matrix functions
    50. The inverse
    51. Exponential and logarithm
    52. The determinant
    53. Jacobians
    54. Sensitivity analysis in regression models
    55. The Hessian matrix
    56. Least squares and best linear unbiased estimation
    57. Maximum likelihood estimation
    58. Inequalities and equalities.

  • Authors

    Karim M. Abadir, Imperial College of Science, Technology and Medicine, London
    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 Econometric Reviews, Econometric Theory, Journal of Financial Econometrics, and Portuguese Economic Journal. He is a Fellow of the Royal Statistical Society.

    Jan R. Magnus, Universiteit van Tilburg
    Jan Magnus is Professor of Econometrics, CentER and Department of Econometrics and Operations Research, Tilburg University, The Netherlands. He has also taught at the University of Amsterdam, The University of British Columbia, The London School of Economics, The University of Montreal, and The European University Institute among other places. His books include Matrix Differential Calculus (with H. Neudecker), Linear Structures, Methodology and Tacit Knowledge (with M. S. Morgan), and Econometrics: A First Course (in Russian with P. K. Katyshev and A. A. Peresetsky). Professor Magnus has written numerous articles in the leading journals, including Econometrica, The Annals of Statistics, The Journal of the American Statistical Association, Journal of Econometrics, Linear Algebra and Its Applications, and The Review of Income and Wealth. He is a Fellow of the Journal of Econometrics, holder of the Econometric Theory Award, and associate editor of The Journal of Economic Methodology, Computational Statistics and Data Analysis, and the Journal of Multivariate Analysis.

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