Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/11424
Title: | Converse to the Parter-Wiener Theorem: the case of non-trees | Authors: | Johnson, Charles R. Duarte, António Leal |
Issue Date: | 2003 | Publisher: | Centro de Matemática da Universidade de Coimbra | Citation: | Pré-Publicações DMUC. 03-31 (2003) | Abstract: | Through a succession of results, it is known that if the graph of an Hermitian matrix A is a tree and if for some index j, λ e σ(A) ∩ σ(A(j)), then there is an index i such that the multiplicity of λ in σ(A(i)) is one more than that in A. We exhibit a converse to this result by showing that it is generally true only for trees. In particular, it is shown that the minimum rank of a positive semidefinite matrix with a given graph G is ≤ n - 2 when G is not a tree. This raises the question of how the minimum rank of a positive semidefinite matrix depends upon the graph in general | URI: | https://hdl.handle.net/10316/11424 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Nacionais |
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File | Description | Size | Format | |
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Converse to the Parter-Wiener Theorem.pdf | 103.32 kB | Adobe PDF | View/Open |
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