Dissertation > Excellent graduate degree dissertation topics show

Maps Preserving Numerical Radius or Cross Norms on 2×2 Matrix Spaces

Author: QianZuXin
Tutor: HouJinChuan
School: Taiyuan University of Technology
Course: Applied Mathematics
Keywords: numerical radius product of matrices cross norm Jordan-semi product self-adjoint matrix symmetric matrix
CLC: O151.21
Type: Master's thesis
Year: 2010
Downloads: 24
Quote: 0
Read: Download Dissertation

Abstract


The linear preserver problem on matrix algebras can be dated back to 19th century and the similar questions on operator algebras on infinite dimensional spaces have also been studied extensively since twety years ago. Recently, the study of linear preserver problems have been generalized to the study of non-linear preserver problems. In this thesis, we discussing the question of characterizing non-linear maps that preserve the numerical radius or a cross norm of product.(1) The unital surjective maps on n×n symmetric matix space with n≥2 which preserve the numerical radius of Jordan semi-product of matrices or preserving a cross norm of Jordan semi-products of matrices are characterized.(2) The unital surjective maps on 2×2 self-adjoint matix space which preserve the numer-ical radius of product or Jordan semi-product of self-adjoint matrices, or preserves a cross norm of products or Jordan semi-products of self-adjoint matrices are characterized. These supplement the corresponding results for n×n self-adjoint matrix space with n≥3.(3) The unital surjective maps on 2×2 matix algebra which preserve the numerical radius of Jordan semi-product of matrices or preserving a cross norm of Jordan semi-products of matrices are characterized. These supplement the corresponding results for n×n matrix algebras with n≥3.

Related Dissertations

  1. The Implementation and Theory of the Tensor Product of Matrices Encryption,TP309.7
  2. Numerical Range of Operator,O177
  3. Maps Preserving Numerical Radius or Cross Norms on 2×2 Matrix Algebras,O151.21
  4. Polar Decomposition and Decomposition of H-normal Matrices with Indefinite Inner Product,O151.21
  5. On the group inverse of the symmetric matrix to maintain,O152
  6. Numerical Analysis of Special Matrices and Preconditioning Techniques for Iteration Solutions of Saddle Point Problems,O151.21
  7. The Solution for Two Kinds Constrained Matrix Equation Problems and Associated Optimal Approximation,O241.5
  8. Homotopy Method for the Inhomogeneous Symmetric Eigenvalue Problem,O151.21
  9. An Improvement and Analysis of the Lanczos Algorithm for Symmetric Matrices Eigenproblem,O241.6
  10. On Parametric Time-Frequency Signal Representation,TN911.6
  11. Theory and Approach on Management of the Very Large-Scale Symmetrical Matrices in Geomatics,P205
  12. The Technique of Acceleration and Preconditioning for Solving Large Symmetric Eigenvalue Problems,O241.6
  13. Solving Large Scale Matrix Eigenvalue Problem with Optimization Methods,O241.6
  14. Iterative Methods for Several Constrained Matrix Equation Problems and Associated Optimal Approximation,O241.6
  15. Total Least Squares Solutions of Inverse Problems for Matrices,O241.6
  16. Solving large asymmetric Eigenproblems Lanczos method both refined version,O241.6
  17. Several special tridiagonal matrix with matrix equation X ~ TAX = B matrix inverse problem,O241.6
  18. Symmetric Eigenvalue Decomposition Hardware Implementation of,TN401
  19. A Study on the Accelerated-strategies of Subspace Iteration Methods,O241.6
  20. The Anti-Bisymmetric Matrices Problem of Matrix Equation AX=B,O241.6

CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
© 2012 www.DissertationTopic.Net  Mobile