数学

部分矩阵逆的填充

  • 赵琳琳 ,
  • 张立华 ,
  • 闫立梅
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  • 德州学院 数学科学学院, 山东 德州 253023

收稿日期: 2015-11-04

  网络出版日期: 2017-01-13

基金资助

山东省高等学校科研发展计划项目(J13LI53)

Inverse completion for partial matrices

  • ZHAO Lin-lin ,
  • ZHANG Li-hua ,
  • YAN Li-mei
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  • College of Mathematical Sciences, Dezhou University, Dezhou Shandong 253023, China

Received date: 2015-11-04

  Online published: 2017-01-13

摘要

利用秩理论和矩阵的广义逆研究了部分矩阵的两类逆的填充问题. 给出了两类逆的填充问题有解的充分必要条件以及解的表示.

关键词: 矩阵填充; 块矩阵; 值域;

本文引用格式

赵琳琳 , 张立华 , 闫立梅 . 部分矩阵逆的填充[J]. 华东师范大学学报(自然科学版), 2016 , 2016(6) : 88 -93 . DOI: 10.3969/j.issn.1000-5641.2016.06.009

Abstract

Two kinds of inverse completion problems for partial matrices were studied by using the rank theory and the Moore-Penrose generalized inverse. Necessary and sufficient conditions for these problems to have a solution were determined and their complete solutions were presented.

参考文献

[ 1 ] BRUALDI R A, HUANG Z J, ZHAN X Z. Singular, nonsingular and bounded rank completions of ACI-matrices[J]. Linear Algebra and Applications, 2010, 433: 1452-1462.
[ 2 ] FIEDLER M, MARKHAM T L. Completing a matrix when certain entries of its inverse are specified[J]. Linear Algebra and Applications, 1986, 74: 225-237.
[ 3 ] DAI H. Completing a symmetric 2 × 2 block matrix and its inverse[J]. Linear Algebra and Applications, 1996, 235: 235-245.
[ 4 ] BARRETT W W, LUNDQUIST M E, JOHNSON C R, et al. Completing a block diagonal matrix with a partially prescribed inverse[J]. Linear Algebra and Applications, 1995, 223/224: 73-87.

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