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<p>The problem of generalized inverses of matrices, and the problem of commutativity of matrices and their generalized inverses have been hot topics in the field of matrix theory. In this paper, we introduce a new kind of special matrices, the BT matrices, which satisfy a matrix <i>A</i> commutes with its BT inverse <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A^{\diamondsuit }\)</EquationSource> </InlineEquation>, and the sufficient and necessary conditions for <i>A</i> to be a BT matrix are proposed. At the end of the paper, we have plotted a relational graph of the existing special matrices.</p>

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Characterizations of the commutativity between a matrix and its BT inverse

  • 期刊论文

  • 发表日期：

    2025年10月22日

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  • Y. F. Gao,
  • T. Y. Zhao,
  • J. M. Xu

摘要

The problem of generalized inverses of matrices, and the problem of commutativity of matrices and their generalized inverses have been hot topics in the field of matrix theory. In this paper, we introduce a new kind of special matrices, the BT matrices, which satisfy a matrix A commutes with its BT inverse \(A^{\diamondsuit }\) , and the sufficient and necessary conditions for A to be a BT matrix are proposed. At the end of the paper, we have plotted a relational graph of the existing special matrices.