Next Article in Journal
A Decision Support System for Dynamic Job-Shop Scheduling Using Real-Time Data with Simulation
Previous Article in Journal
Variational Approaches for Lagrangian Discrete Nonlinear Systems
Article Menu
Issue 3 (March) cover image

Export Article

Open AccessArticle
Mathematics 2019, 7(3), 277; https://doi.org/10.3390/math7030277

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

School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China
*
Author to whom correspondence should be addressed.
Received: 25 January 2019 / Revised: 9 March 2019 / Accepted: 13 March 2019 / Published: 19 March 2019
(This article belongs to the Section Mathematics and Computers Science)
  |  
PDF [234 KB, uploaded 19 March 2019]
  |  

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 } . View Full-Text
Keywords: forward order law; generalized inverse; maximal rank; matrix product; generalized Schur complement forward order law; generalized inverse; maximal rank; matrix product; generalized Schur complement
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Xiong, Z.; Liu, Z. The Forward Order Law for Least Squareg-Inverse of Multiple Matrix Products. Mathematics 2019, 7, 277.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top