The Forward Order Law for Least Square g -Inverse of Multiple Matrix Products

Zhiping Xiong and Zhongshan Liu
Additional contact information
Zhiping Xiong: School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China
Zhongshan Liu: School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China

Mathematics, 2019, vol. 7, issue 3, 1-10

Abstract: The generalized inverse has many important applications in the aspects of the theoretic research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the forward order laws for the generalized inverse of the matrix product. In this paper, by using the extremal ranks of the generalized Schur complement, we obtain some necessary and sufficient conditions for the forward order laws A 1 { 1 , 3 } A 2 { 1 , 3 } ? A n { 1 , 3 } ⊆ ( A 1 A 2 ? A n ) { 1 , 3 } and A 1 { 1 , 4 } A 2 { 1 , 4 } ? A n { 1 , 4 } ⊆ ( A 1 A 2 ? A n ) { 1 , 4 } .

Keywords: forward order law; generalized inverse; maximal rank; matrix product; generalized Schur complement (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/3/277/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/3/277/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:3:p:277-:d:215183

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().