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

Author

Listed:
  • 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)

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 } .

Suggested Citation

  • Zhiping Xiong & Zhongshan Liu, 2019. "The Forward Order Law for Least Square g -Inverse of Multiple Matrix Products," Mathematics, MDPI, vol. 7(3), pages 1-10, March.
  • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:277-:d:215183
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    Cited by:

    1. Dilan Ahmed & Mudhafar Hama & Karwan Hama Faraj Jwamer & Stanford Shateyi, 2019. "A Seventh-Order Scheme for Computing the Generalized Drazin Inverse," Mathematics, MDPI, vol. 7(7), pages 1-10, July.

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