Principal Submatrices of a Hermitian Matrix |
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| Authors: | Chi-Kwong Li Yiu-Tung Poon |
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| Institution: | 1. Department of Mathematics , College of William and Mary , P.O. Box 8795, Williamsburg , Virginia , 23187-8795 , USA;2. Department of Mathematics , Iowa State University , Ames , Iowa , 50011 , USA;3. Department of Mathematics , The Hong Kong Institute of Education , 10 Lo Ping Road, Tai Po, N.T. , Hong Kong |
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| Abstract: | Suppose k 1 ,<, k m and n are positive integers such that k 1 + … + k m h n . We characterize those k i × k i Hermitian matrices A i , i = 1, < , m that can appear as diagonal blocks of an n × n Hermitian matrix C with prescribed eigenvalues. The characterization will be given in terms of the eigenvalues of C and A i , i = 1, <, m . Our results extend those of Thompson and Freede, Horn, Fan and Pall. |
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| Keywords: | Hermitian Matrices Singular Values Eigenvalues |
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