论文标题
张量的加权摩尔 - 柔性的数值范围
Numerical range for weighted Moore-Penrose inverse of tensor
论文作者
论文摘要
本文首先介绍了通过爱因斯坦产品的张量的加权奇异值分解（WSVD）的概念。然后使用WSVD来计算任意订单张量的加权摩尔 - 柔性倒数。然后，我们为均衡的平方张量和加权张量标准定义了加权正常张量的概念。最后，我们将其应用于研究数值范围的理论，用于加权的摩尔 - 碳纤维的均匀平方张量，并利用其几种特性。我们还将在矩阵设置中获得一些新的结果，这些结果将一些现有结果概括为特定情况。
This article first introduces the notion of weighted singular value decomposition (WSVD) of a tensor via the Einstein product. The WSVD is then used to compute the weighted Moore-Penrose inverse of an arbitrary-order tensor. We then define the notions of weighted normal tensor for an even-order square tensor and weighted tensor norm. Finally, we apply these to study the theory of numerical range for the weighted Moore-Penrose inverse of an even-order square tensor and exploit its several properties. We also obtain a few new results in the matrix setting that generalizes some of the existing results as particular cases.
