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Level: BSc, MSci, MSc
Title: Weyl's inequality
Supervisor:

Dr Oscar Bandtlow
Research Area: Dynamical Systems and Statistical Physics
Description:

Weyl's inequality is a classical inequality between the eigenvalues and the singular values of a matrix. It plays an important role in the study of the eigenvalue distribution of compact operators, an active area of current research. The aim of the project is to obtain familiarity with the inequality, and then to explore consequences and generalisations.
Further Reading:
  • H. Weyl, Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci. U.S.A. 35 (1949) 408–411.
  • J. R. Retherford, Hilbert Space: Compact Operators and the Trace Theorem. Cambridge Univ. Press, 1993.
  • R. Bhatia, Matrix Analysis. Springer, New York, 1997.
Key Modules:

MTH5112 Linear Algebra I

MTH5104 Convergence and Continuity

MTH5105 Differential and Integral Analysis
Other Information:
Current Availability: Yes