Expressions on generalized inverses of the Schur complement of a 2×2 block matrix
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摘要: 本文主要研究了不同条件下同一个2x2 分块矩阵 M=\left( \begin{array}{cc} A B \\ C D \\ \end{array} \right) 中 Schur 补的广义逆 S=A-BD^{-}C 不同的表示形式, 特别地, 当 M 是一个半正定 Hermite 阵时, 可以得到关于 Schur 补的广义逆的一些新形式, 并由此得到一些推论.Abstract: This article investigates various expressions for the generalized inverses of the Schur complement S = A BDC of a 2 2 block matrix M = A B C D ! under different conditions. Moreover, we give some new results for the generalized inverses of the Schur complement when M is positive semidefinite. Besides, some conclusions are obtained directly from our results.
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Key words:
- 2 2 block matrix /
- generalized inverse /
- Schur complement
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