Publicação
A Fiedler's type characterization of band matrices
| Resumo: | Let K be a field and p an integer positive number. We denote by Bpn (K) the set of n-by-n symmetric band matrices of bandwidth 2p − 1, i.e., if A = [aij ] ∈ Bpn (K) then aij = 0 if |i − j| > p − 1. Let b Bpn (K) be the set of matrices from Bpn (K) in which the entries (i, j), |i − j| = p − 1, are different from zero. Let A be a n-by-n symmetric matrix with entries from K; and p such that 3 6 p 6 n. We will show that: rank(A + B) > n − p + 1, for every B ∈ Bp−1 n (K), if and only if A ∈ b Bpn (K). |
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| Autores principais: | Bento, Américo |
| Outros Autores: | Duarte, António Leal |
| Assunto: | Band matrices Rank Completions problems |
| Ano: | 2004 |
| País: | Portugal |
| Tipo de documento: | outro |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Coimbra |
| Idioma: | inglês |
| Origem: | Estudo Geral - Universidade de Coimbra |
| Resumo: | Let K be a field and p an integer positive number. We denote by Bpn (K) the set of n-by-n symmetric band matrices of bandwidth 2p − 1, i.e., if A = [aij ] ∈ Bpn (K) then aij = 0 if |i − j| > p − 1. Let b Bpn (K) be the set of matrices from Bpn (K) in which the entries (i, j), |i − j| = p − 1, are different from zero. Let A be a n-by-n symmetric matrix with entries from K; and p such that 3 6 p 6 n. We will show that: rank(A + B) > n − p + 1, for every B ∈ Bp−1 n (K), if and only if A ∈ b Bpn (K). |
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