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

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Bueno, MI (Author) Other; Susana Borges Furtado (Author) FEP

Journal

Title: Linear Algebra and Its Applications

Vol. 702

Pages: 122-142

ISSN: 0024-3795

Publisher: Elsevier

Indexing

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Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21