It is proved that any \(B_{\pi }^R\)-matrix has positive determinant. For \({\pi >0}\), norm bounds for the inverses of \(B_{\pi }^R\)-matrices and error bounds for linear complementarity problems associated with \(B_{\pi }^R\)-matrices are provided. In this last case, the bounds are simpler than previous bounds and also have the advantage that they can be used without previously knowing whether we have a \(B_{\pi }^R\)-matrix. Some numerical examples show that these new bounds can be considerably sharper than previous ones.

中文翻译：

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$$ B _ {\ pi} ^ R $$ BπR-矩阵的线性互补问题的误差界

证明任何\（B _ {\ pi} ^ R \）-矩阵都具有正行列式。对于\（{\ pi> 0} \），\（B _ {\ pi} ^ R \）的逆的范数界和与\（B _ {\ pi} ^ R \ ）-提供了矩阵。在后一种情况下，边界比以前的边界更简单，并且具有以下优点：可以在不事先知道我们是否具有\（B _ {\ pi} ^ R \）-矩阵的情况下使用它们。一些数值示例表明，这些新界限可能比以前的界限更加清晰。