Matrix Algebra by K.M. Abadir and Jan R. Magnus

 Price 26.99 Pound

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.

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.