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The research is partly supported by Project MTM2010-18057, Ministerio de Ciencia e Innovacion of Spain.

Analysis of institutional authors

Castro-Gonzalez, N.AuthorMartinez-Serrano, M. F.AuthorRobles, J.Author

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June 9, 2019
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Expressions for the Moore-Penrose inverse of block matrices involving the Schur complement

Publicated to:Linear Algebra And Its Applications. 471 353-368 - 2015-04-15 471(), DOI: 10.1016/j.laa.2015.01.003

Authors: Castro-Gonzalez, N.; Martinez-Serrano, M. F.; Robles, J.;

Affiliations

Univ Politecn Madrid, ETS Ingenieros Informat, Dept Matemat Aplicada, E-28660 Madrid, Spain - Author

Abstract

We present a formula for the Moore-Penrose inverse of a matrix of the form M = XNY, where X and Y are nonsingular. Based on this result, we develop explicit expressions for the Moore Penrose inverse of a 2 x 2 complex block matrix M. We recover the cases when a Schur complement in M is either equal to zero or nonsingular. Some applications to banded matrices and bordered matrices are indicated. (C) 2015 Elsevier Inc. All rights reserved.

Keywords

Block matrixBordered matrixGeneralized inversesMoore-penrose inversePartitioned matrixSchur complement

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Linear Algebra And Its Applications due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2015, it was in position 64/312, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.25. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Weighted Average of Normalized Impact by the Scopus agency: 2.17 (source consulted: FECYT Feb 2024)
  • Field Citation Ratio (FCR) from Dimensions: 12.78 (source consulted: Dimensions Jul 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-07-27, the following number of citations:

  • WoS: 10
  • Scopus: 18

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-27:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 12 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (CASTRO GONZALEZ, BLANCA NIEVES) and Last Author (ROBLES SANTAMARTA, JUAN).