The Explicit Formula for the Moore-Penrose Inverse of a 2×2 Block Matrix

ZENG Min, YUAN Yong-xin

doi:10.13371/j.cnki.chin.q.j.m.2023.04.007

Chinese Quarterly Journal of Mathematics >

2023 , Vol. 38 >Issue 4: 401 - 409

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2023.04.007

The Explicit Formula for the Moore-Penrose Inverse of a 2×2 Block Matrix

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School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

ZENG Min (1999-), female, native of Jingzhou, Hubei, postgraduate student of Hubei Normal University, engages in computational mathematics; YUAN Yong-xin (1966-), male, native of Zhenjiang, Jiangsu, professor of Hubei Normal University, engages in computational mathematics.

Received date: 2022-05-10

Online published: 2023-12-30

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Abstract

The representation for the Moore-Penrose inverse of the matrix
A B
C D
is derived by using the solvability theory of linear equations, where A∈C^m×n, B∈C^m×p, C∈C^q×nand D∈C^q×p, with which some special cases are discussed.

Key words： Block matrix; Moore-Penrose inverse; Linear equation

Cite this article

ZENG Min, YUAN Yong-xin . The Explicit Formula for the Moore-Penrose Inverse of a 2×2 Block Matrix[J]. Chinese Quarterly Journal of Mathematics, 2023 , 38(4) : 401 -409 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.007

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