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.
anti-Hermitian generalized anti-Hamiltonian matrix algebra inverse eigenvalue problem optimal approximation
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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
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
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
Ben-Israel A, Greville T N E. Generalized Inverse: Theory and Applications [M]. New York: John Wiley Sons, 1974.zbMATHGoogle Scholar
Cheng E W. Introduction to Approximation Theory [M]. Mc Graw-Hill Book Col, 1966.Google Scholar