Abstract This study examines several generic properties of weighted consistent projections and indicators of inconsistency in an arbitrary finite dimensional inner product space of square matrices. In the case of weighted Frobenius inner products we present explicit formulae for them in terms of the matrix entries and weights. It extends the recent results, due to Koczkodaj et al. [Fund. Inform. 172 (2020) 379–397], to positive matrices in pairwise comparisons. Moreover, we discuss the possibilities of a proper choice of the inner product weights for numerical applications based on the orthogonal consistent projections.

中文翻译：

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成对比较中的一致预测和指标

摘要 本研究检验了方阵的任意有限维内积空间中加权一致投影和不一致指标的几个通用属性。在加权 Frobenius 内积的情况下，我们根据矩阵项和权重为它们提供明确的公式。由于 Koczkodaj 等人，它扩展了最近的结果。[基金。通知。172 (2020) 379–397]，成对比较中的正矩阵。此外，我们讨论了基于正交一致投影为数值应用正确选择内积权重的可能性。