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<p>The aim of the paper is to utilize the formulae for the powers of two anti-triangular block matrices to develop explicit representations for the Drazin inverse of <i>P</i> + <i>Q</i> under specific conditions. These findings are further applied to derive the expressions for the Drazin inverse of a modified matrix <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A-CD^dB\)</EquationSource> </InlineEquation> of <i>A</i>, extending and unifying many existing results.</p>

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Some formulas on the Drazin inverse for additive results of matrices and modified matrix

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Daochang Zhang,
  • Yue Zhao,
  • Dijana Mosić

摘要

The aim of the paper is to utilize the formulae for the powers of two anti-triangular block matrices to develop explicit representations for the Drazin inverse of P + Q under specific conditions. These findings are further applied to derive the expressions for the Drazin inverse of a modified matrix \(A-CD^dB\) of A, extending and unifying many existing results.