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Endlich dimensionale Vektorräume von Halmos 1974 ALT VINTAGE MATHEMATIK MATHEMATIK
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Endlich dimensionale Vektorräume von Halmos 1974 ALT VINTAGE MATHEMATIK MATHEMATIK
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Endlich dimensionale Vektorräume von Halmos 1974 ALT VINTAGE MATHEMATIK MATHEMATIK

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    Artikelzustand
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    Hinweise des Verkäufers
    “Signed by previous owner, else all pages clean & unmarked. Please see photos for complete condition ...
    Personalized
    No
    Country/Region of Manufacture
    United States
    ISBN
    9780387900933
    Kategorie

    Über dieses Produkt

    Product Identifiers

    Publisher
    Springer New York
    ISBN-10
    0387900934
    ISBN-13
    9780387900933
    eBay Product ID (ePID)
    155769

    Product Key Features

    Number of Pages
    VIII, 202 Pages
    Publication Name
    Finite-Dimensional Vector Spaces
    Language
    English
    Subject
    Transformations, Algebra / General, Vector Analysis
    Publication Year
    1974
    Features
    Reprint
    Type
    Textbook
    Author
    P. R. Halmos
    Subject Area
    Mathematics
    Series
    Undergraduate Texts in Mathematics Ser.
    Format
    Hardcover

    Dimensions

    Item Height
    0.3 in
    Item Weight
    37 Oz
    Item Length
    9.3 in
    Item Width
    6.1 in

    Additional Product Features

    Edition Number
    2
    Intended Audience
    Scholarly & Professional
    LCCN
    74-010688
    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 Volumes
    1 vol.
    Illustrated
    Yes
    Edition Description
    Reprint
    Table Of Content
    I. 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 Number
    QA150-272

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