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Girko

Theory of Random Determinants

Medium: Buch
ISBN: 978-0-7923-0233-9
Verlag: Springer Netherlands
Erscheinungstermin: 30.09.1990
Lieferfrist: bis zu 10 Tage
'Et mm., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point all':'' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf IIClI.t to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics.'; 'One service logic has rendered com­ puter science.'; 'One service category theory has rendered mathematics.'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Produkteigenschaften


  • Artikelnummer: 9780792302339
  • Medium: Buch
  • ISBN: 978-0-7923-0233-9
  • Verlag: Springer Netherlands
  • Erscheinungstermin: 30.09.1990
  • Sprache(n): Englisch
  • Auflage: 1990
  • Serie: Mathematics and its Applications
  • Produktform: Gebunden, HC runder Rücken kaschiert
  • Gewicht: 1215 g
  • Seiten: 678
  • Format (B x H x T): 160 x 241 x 43 mm
  • Ausgabetyp: Kein, Unbekannt

Autoren/Hrsg.

Autoren

Girko, V. L.

1. Generalized Wishart Density and Integral Representation for Determinants.- 2. Moments of Random Matrix Determinants.- 3. Distribution of Eigenvalues and Eigenvectors of Random Matrices.- 4. Inequalities for Random Determinants.- 5. Limit Theorems for the Borel Functions of Independent Random Variables.- 6. Limit Theorems of the Law of Large Numbers and Central Limit Theorem Types for Random Determinants.- 7. Accompanying Infinitely Divisible Laws for Random Determinants.- 8. Integral Representation Method.- 9. The Connection between the Convergence of Random Determinants and the Convergence of Functionals of Random Functions.- 10. Limit Theorems for Random Gram Determinants.- 11. The Determinants of Toeplitz and Hankel Random Matrices.- 12. Limit Theorems for Determinants of Random Jacobi Matrices.- 13. The Fredholm Random Determinants.- 14. The Systems of Linear Algebraic Equations with Random Coefficients.- 15. Limit Theorems for the Solution of the Systems of Linear Algebraic Equations with Random Coefficients.- 16. Integral Equations with Random Degenerate Kernels.- 17. Random Determinants in the Spectral Theory of Non-Self-Adjoint Random Matrices.- 18. The Distribution of Eigenvalues and Eigenvectors of Additive Random Matrix-Valued Processes.- 19. The Stochastic Ljapunov Problem for Systems of Stationary Linear Differential Equations.- 20. Random Determinants in the Theory of Estimation of Parameters of Some Systems.- 21. Random Determinants in Some Problems of Control Theory of Stochastic Systems.- 22. Random Determinants in Some Linear Stochastic Programming Problems.- 23. Random Determinants in General Statistical Analysis.- 24. Estimate of the Solution of the Kolmogorov-Wiener Filter.- 25. Random Determinants in Pattern Recognition.- 26. Random Determinantsin the Experiment Design.- 27. Random Determinants in Physics.- 28. Random Determinants in Numerical Analysis.- References.