Picture 1 of 1

Stock photo

Finite-Dimensional Vector Spaces by P R Halmos: New - Picture 1 of 1

Undergraduate Texts in Mathematics Ser.: Finite-Dimensional Vector Spaces by P. R. Halmos (1974, Hardcover)

5.01 product rating

AlibrisBooks (482666)

98.9% positive Feedback

Price:

US $69.25

Approximately£51.55

+ $20.19 postage

Estimated delivery Fri, 31 Oct - Fri, 7 Nov

Returns:

30 days return. Buyer pays for return postage. If you use an eBay delivery label, it will be deducted from your refund amount.

Condition:

New

New Hard cover

About this product

Product Identifiers

PublisherSpringer New York

ISBN-100387900934

ISBN-139780387900933

eBay Product ID (ePID)155769

Product Key Features

Number of PagesVIII, 202 Pages

Publication NameFinite-Dimensional Vector Spaces

LanguageEnglish

SubjectTransformations, Algebra / General, Vector Analysis

Publication Year1974

FeaturesReprint

TypeTextbook

AuthorP. R. Halmos

Subject AreaMathematics

SeriesUndergraduate Texts in Mathematics Ser.

FormatHardcover

Dimensions

Item Height0.3 in

Item Weight37 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Edition Number2

Intended AudienceScholarly & Professional

LCCN74-010688

Reviews"The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher". Zentralblatt fuer Mathematik, "This is a classic but still useful introduction to modern linear algebra. It is primarily about linear transformations ... . It's also extremely well-written and logical, with short and elegant proofs. ... The exercises are very good, and are a mixture of proof questions and concrete examples. The book ends with a few applications to analysis ... and a brief summary of what is needed to extend this theory to Hilbert spaces." (Allen Stenger, MAA Reviews, maa.org, May, 2016) "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." Zentralblatt für Mathematik, "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." Zentralblatt für Mathematik

Number of Volumes1 vol.

IllustratedYes

Edition DescriptionReprint

Table Of ContentI. Spaces.- 1. Fields.- 2. Vector spaces.- 3. Examples.- 4. Comments.- 5. Linear dependence.- 6. Linear combinations.- 7. Bases.- 8. Dimension.- 9. Isomorphism.- 10. Subspaces.- 11. Calculus of subspaces.- 12. Dimension of a subspace.- 13. Dual spaces.- 14. Brackets.- 15. Dual bases.- 16. Reflexivity.- 17. Annihilators.- 18. Direct sums.- 19. Dimension of a direct sum.- 20. Dual of a direct sum.- 21. Quotient spaces.- 22. Dimension of a quotient space.- 23. Bilinear forms.- 24. Tensor products.- 25. Product bases.- 26. Permutations.- 27. Cycles.- 28. Parity.- 29. Multilinear forms.- 30. Alternating forms.- 31. Alternating forms of maximal degree.- II. Transformations.- 32. Linear transformations.- 33. Transformations as vectors.- 34. Products.- 35. Polynomials.- 36. Inverses.- 37. Matrices.- 38. Matrices of transformations.- 39. Invariance.- 40. Reducibility.- 41. Projections.- 42. Combinations of pro¬jections.- 43. Projections and invariance.- 44. Adjoints.- 45. Adjoints of projections.- 46. Change of basis.- 47. Similarity.- 48. Quotient transformations.- 49. Range and null-space.- 50. Rank and nullity.- 51. Transformations of rank one.- 52. Tensor products of transformations.- 53. Determinants.- 54. Proper values.- 55. Multiplicity.- 56. Triangular form.- 57. Nilpotence.- 58. Jordan form.- III. Orthogonality.- 59. Inner products.- 60. Complex inner products.- 61. Inner product spaces.- 62. Orthogonality.- 63. Completeness.- 64. Schwarz's inequality.- 65. Complete orthonormal sets.- 66. Projection theorem.- 67. Linear functionals.- 68. Parentheses versus brackets.- 69. Natural isomorphisms.- 70. Self-adjoint transformations.- 71. Polarization.- 72. Positive transformations.- 73. Isometries.- 74. Change of orthonormal basis.- 75. Perpendicular projections.- 76. Combinations of perpendicular projections.- 77. Complexification.- 78. Characterization of spectra.- 79. Spectral theorem.- 80. Normal transformations.- 81. Orthogonal transformations.- 82. Functions of transformations.- 83. Polar decomposition.- 84. Commutativity.- 85. Self-adjoint transformations of rank one.- IV. Analysis.- 86. Convergence of vectors.- 87. Norm.- 88. Expressions for the norm.- 89. Bounds of a self-adjoint transformation.- 90. Minimax principle.- 91. Convergence of linear transformations.- 92. Ergodic theorem.- 93. Power series.- Appendix. Hilbert Space.- Recommended Reading.- Index of Terms.- Index of Symbols.

Synopsis"The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher". Zentralblatt fuer Mathematik, "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all, this is an excellent work, of equally high value for both student and teacher." Zentralblatt f r Mathematik, "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all, this is an excellent work, of equally high value for both student and teacher." Zentralblatt für Mathematik, "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." Zentralblatt für Mathematik

LC Classification NumberQA150-272