On the rank structure of the Moore-Penrose inverse of singular k-banded matrices

• Tipo: Artigo em Revista Científica Internacional
• Data: 2024

Autores

Bueno, MI (Autor) Outra; Susana Borges Furtado (Autor) FEP

Revista

Título: Linear Algebra and Its Applications

Vol. 702

Páginas: 122-142

ISSN: 0024-3795

Editora: Elsevier

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-016-VF0

DOI: 10.1016/j.laa.2024.08.011

Abstract (EN): It is well-established that, for an n x n singular k- banded complex matrix B, the submatrices of the Moore-Penrose inverse B- dagger of B located strictly below (resp. above) its k th superdiagonal (resp. kth subdiagonal) have a certain bounded rank s depending on n, k and rankB. B. In this case, B( dagger )is said to satisfy a semiseparability condition. In this paper our focus is on singular strictly k- banded complex matrices B, and we show that the Moore-Penrose inverse of such a matrix satisfies a stronger condition, called generator representability. This means that there exist two matrices of rank at most s whose parts strictly below the kth diagonal (resp. above the k th subdiagonal) coincide with the same parts of B- dagger . When n >= 3 k, we prove that s is precisely the minimum rank of these two matrices. We also illustrate through examples that when n < 3k k those matrices may have rank less than s.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 21