We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on triangular decomposition of block matrices. The case of inverting matrices over a ring that is neither formally real nor formally complex was inspired by Gonzalez-Vega et al.

翻译：本文研究了递归分块矩阵的若干线性代数算法。该表示方法具有实用的应用价值和理论意义。我们总结了分块矩阵求逆的一些已有结果，并提出了分块矩阵三角分解的相关结论。关于在既非形式实也非形式复的环上矩阵求逆的情形，其研究灵感来源于Gonzalez-Vega等人的工作。