Journal of Jianghan University (Natural Science Edition) ›› 2019, Vol. 47 ›› Issue (5): 389-394.doi: 10.16389/j.cnki.cn42-1737/n.2019.05.001

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Some Notes on {1，3}-Inverses，{1，4}-Invereses and Moore-Penrose Inverse of Matrix Products in Rings

KE Yuanyuan1，LI Yizheng2   

  1. 1. School of Mathematics and Computer Science，Jianghan University，Wuhan 430056，Hubei，China；2. School of Mathematics and Statistics，Guizhou University of Finance and Economics，Guiyang 550025，Guizhou，China
  • Published:2019-10-08

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Abstract: In 2015，N. Castro-Gonzalez gave the necessary and sufficient conditions for the existence of a {1，3}-inverese of PA，{1，4}-inverse of AQ，and the Moore-Penrose inverse of a matrix product PAQ in rings when P is invertible，in this paper，the necessary and sufficient conditions for the existence of a {1，3}-inverese of PA，{1，4}-inverse of AQ，and the Moore-Penrose inverse of a matrix product PAQ in rings are characterized under the condition P′PA =A =AQQ′ .

Key words: generalized inverses, {1，3}-inverses, {1，4}-inverses, Moore-Penrose inverse

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