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<p>It<?tk 1?> is known the connection between the best approximation and Moore–Penrose invertibility. In particular, the best approximation pair of two affine subspaces is related to generalized invertibility of a block matrix of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left[ \begin{array}{cc} I_n &amp; A\\ B &amp; I_m\end{array}\right] \)</EquationSource> </InlineEquation>. In this paper, we address the Moore–Penrose inverse and the group inverse of a block matrix <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\left[ \begin{array}{cc} I_n &amp; A\\ B &amp; D\end{array}\right] \)</EquationSource> </InlineEquation>.</p>

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Generalized inverses of special matrices partitioned into blocks

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Regina De Almeida,
  • Paula Catarino,
  • Pedro Patrício,
  • M. A. Facas Vicente,
  • José Vitória

摘要

It is known the connection between the best approximation and Moore–Penrose invertibility. In particular, the best approximation pair of two affine subspaces is related to generalized invertibility of a block matrix of the form \(\left[ \begin{array}{cc} I_n & A\\ B & I_m\end{array}\right] \) . In this paper, we address the Moore–Penrose inverse and the group inverse of a block matrix \(\left[ \begin{array}{cc} I_n & A\\ B & D\end{array}\right] \) .