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Linear algebra

Author: V I Smirnov; Donald E Brown
Publisher: Oxford : Pergamon Press, [1964]
Series: Course of higher mathematics, v. 3, pt. 1.; International series of monographs in pure and applied mathematics, v. 59.
Edition/Format:   eBook : Document : English
Database:WorldCat
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Genre/Form: Electronic books
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
ISBN: 9781483152592 1483152596
OCLC Number: 953660390
Notes: Includes index.
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.

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