Acta mathematica scientia,Series B ›› 2005, Vol. 25 ›› Issue (3): 492-504.

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THE BI-SELF-CONJUGATE AND NONNEGATIVE DEFINITE SOLUTIONS TO THE INVERSE EIGENVALUE PROBLEM OF QUATERNION MATRICES

 CHU Yu-Meng   

  • Online:2005-07-20 Published:2005-07-20
  • Supported by:

    This work is supported by the NSF of China (10471039, 10271043) and NSF of
    Zhejiang Province (M103087).

Abstract:


The main aim of this paper is to discuss the following  two problems:  \\
 Problem I: Given  XHn×m (the set of all n×m quaternion matrices),
 Λ=diag(λ1,, λm)Hm×m,
 find ABSHn×n  such that AX=XΛ, where BSHn×n 
 denotes the set of all n×n quaternion matrices which are bi-self-conjugate and nonnegative definite.\\
 ProblemⅡ: Given  BHn×m, find ¯BSE  such that
 B¯BQ=minASEBAQ,
 where SE is the solution set of problem Ⅰ,  Q is the
 quaternion matrix norm. The necessary and sufficient conditions for SE  being nonempty are obtained.
 The general form of elements in  SE and the expression of the unique solution ¯B 
 of problem Ⅱ are given.
 

Key words: Conjugate, inverse eigenvalue problem, quaternion matrix

CLC Number: 

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