Solvability conditions for algebra inverse eigenvalue problem over set of anti-Hermitian generalized anti-Hamiltonian matrices

  • Zhang Zhong-zhi Email author
  • Han Xu-li 


By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-Hermitian generalized anti-Hamiltonian matrices, and obtain a general expression of the solution to this problem. By using the properties of the orthogonal projection matrix, we also obtain the expression of the solution to optimal approximate problem of an n×n complex matrix under spectral restriction.

Key words

anti-Hermitian generalized anti-Hamiltonian matrix algebra inverse eigenvalue problem optimal approximation 

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  1. [1]
    Li N. A matrix inverse eigenvalue problem and its application [J]. Linear Algebra and its Application, 1997, 266: 143–152.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Li N, Chu K W E. Designing Hopfield neural network via pole assignment[J]. International Journal of Systems Science, 1994, 25:669–681.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Joseph K T. Inverse eigenvalue problem in structural design[J]. AIAA J, 1992, 10:2890–2896.CrossRefGoogle Scholar
  4. [4]
    Baruch M. Optimization procedure to correct stiffness and flexibility matrices using vibration tests[J]. AIAA J, 1978, 16 (11): 1208–1210.CrossRefGoogle Scholar
  5. [5]
    Berman A, Nagy E J. Improvement of a large analytical model using test data[J]. AIAA J, 1983, 21(8): 1168–1173.CrossRefGoogle Scholar
  6. [6]
    Borges C F, Frezza R, Gragg W B. Some inverse eigenproblems for Jacobi and Arrow matrices [J]. NumerLinear Algebra Appl, 1995, 2:195–203.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Woodgate K G. Least-squares solution of over positive semi-definite symmetric P[J]. Linear Algebra Appl, 1996, 245:171–190.MathSciNetCrossRefGoogle Scholar
  8. [8]
    XIE Dong-xiu. Least-squares solution for inverse eigenpair problem of nonnegative definite matrices[J]. Computers and Mathematics with Applications, 2000, 40:1241–1251.MathSciNetCrossRefGoogle Scholar
  9. [9]
    XIE Dong-xiu, ZHANG Lei, XU Xi-yan. The solvability conditions for the inverse problem of bisymmetric nonnegative definite matrices [J]. J Comput Math, 2000, 18(6):597–608.MathSciNetzbMATHGoogle Scholar
  10. [10]
    XIE Dong-xiu, ZHANG Lei. Least-squares solutions of inverse problems for anti-symmetric matrices[J]. Journal of Engineering Mathematic, 1993, 10(4):25–34. (in Chinese)Google Scholar
  11. [11]
    Ben-Israel A, Greville T N E. Generalized Inverse: Theory and Applications [M]. New York: John Wiley Sons, 1974.zbMATHGoogle Scholar
  12. [12]
    Cheng E W. Introduction to Approximation Theory [M]. Mc Graw-Hill Book Col, 1966.Google Scholar

Copyright information

© Central South University 2005

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceCentral South UniversityChangshaChina
  2. 2.Department of MathematicsDongguan University of TechnologyDongguanChina

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