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|Additional Physical Format:||Print version:
Smirnov, V. I.
A Course of Higher Mathematics : Linear Algebra : Adiwes International Series in Mathematics, Volume 3P1
Kent : Elsevier Science,c2016
|Material Type:||Document, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
V I Smirnov; Donald E Brown
Description based upon print version of record.
78. Regular representations of groups
|Description:||1 online resource (335 p.)|
|Contents:||Front Cover; A Course of Higher Mathematics, Part 1; Copyright Page; Table of Contents; INTRODUCTION; PREFACE TO THE FOURTH RUSSIAN EDITION; CHAPTER I. DETERMINANTS. THE SOLUTION OF SYSTEMS OF EQUATIONS; 1. Properties of determinants; 2. The solution of systems of equations; CHAPTER II. LINEAR TRANSFORMATIONS AND QUADRATIC FORMS; 20. Coordinate transformations in three-dimensional space; 21. General linear transformations of real three-dimensional space; 22. Covariant and contravariant affine vectors; 23. Tensors; 24. Examples of affine orthogonal tensors 25. The case of n-dimensional complex space26. Basic matrix calculus; 27. Characteristic roots of matrices and reduction to canonical form ; 28. Unitary and orthogonal transformations; 29. Buniakowski's inequality; 30. Properties of scalar products and norms; 31. Orthogonalization of vectors; 32. Transformation of a quadratic form to a sum of squares ; 33. The case of multiple roots of the characteristic equation ; 34. Examples; 35. Classification of quadratic forms ; 36. Jacobi's formula ; 37. The simultaneous reduction of two quadratic forms to sums of squares ; 38. Small vibrations 39. Extremal properties of the eigenvalues of quadratic forms40. Hermitian matrices and Hermitian forms ; 41. Commutative Hermitian matrices ; 42. The reduction of unitary matrices to the diagonal form ; 43. Projection matrices; 44. Functions of matrices ; 45. Infinite-dimensional space; 46. The convergence of vectors; 47. Complete systems of mutually orthogonal vectors ; 48. Linear transformations with an infinite set of variables ; 49. Functional space; 50. The connection between functional and Hilbert space ; 51. Linear functional operators CHAPTER III. THE BASIC THEORY OF GROUPS AND LINEAR REPRESENTATIONS OF GROUPS52. Groups of linear transformations; 53. Groups of regular polyhedra; 54. Lorentz transformations ; 55. Permutations ; 56. Abstract groups ; 57. Subgroups ; 58. Classes and normal subgroups; 59. Examples ; 60. Isomorphic and homomorphic groups ; 61. Examples; 62. Stereographic projections; 63. Unitary groups and groups of rotations; 64. The general linear group and the Lorentz group; 65. Representation of a group by linear transformations; 66. Basic theorems 67. Abelian groups and representations of the first degree68. Linear representations of the unitary group in two variables ; 69. Linear representations of the rotation group; 70. The theorem on the simplicity of the rotation group ; 71. Laplace's equation and linear representations of the rotation group ; 72. Direct matrix products; 73. The composition of two linear representations of a group ; 74. The direct product of groups and its linear representations ; 75 Decomposition of the composition Dj X Dj, of linear representations of the rotation group; 76. Orthogonality; 77. Characters|
|Series Title:||Course of higher mathematics, v. 3, pt. 1.; International series of monographs in pure and applied mathematics, v. 59.|
|Responsibility:||translated by D.E. Brown.|