An earlier proof of this formula for four-vector operators is extended to symmetric and antisymmetric rank-two tensor operators. The matrix elements of all irreducible rank-two tensor operators are tabulated. Finally we generalize the results for the group SL 2, C extended by parity....
A nonnegative tensor P has nonnegative rank at most 2 if and only if P is supermodular and has flattening rank at most 2. Here, flattening means picking any subset A of with and writing the tensor P as an ordinary matrix with rows and columns. The flattening rank of P (also called ...
It has 2 Axis It has aRank of 2 It is a 2-dimensional Tensor Real Tensors Technically, all of the above are tensors, but when we speak of tensors, we generally speak of matrices with a dimension larger than 2 (R > 2).
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 <= j <= k-1, and k rank-2 Killing tensors, giving k con...
Since the strain tensor is defined as a symmetric tensor of second rank, at least 6 reflections have to be analysed concerning their precise reflection position. The procedure for the reflection position determination and the necessary correction factors to be applied are described in paragraph 2.184...
rank n. 1.[C,U] 等级;地位,身份 2.[C,U] 社会阶层;军阶,军衔 3.[U] 高地位,高身份,显贵 4.[C] 排,横列;【军】行列 5. 队伍;军队;士兵 6.[U]] tensor n. 张肌,张量 first rank adj. 第一流的,最佳的,优秀的 rank and filer n. 普通士兵 top rank adj. 第一流的,最受赏识的...
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2、tensor 的三个属性 2.1 Rank 秩 秩就是张量中存在的维度的数目,或者说从张量中获取一个元素所需要的索引数,例如矩阵、二维数组、二维张量,它们的秩都是 2 2.2 Axis(复数 为 Axes) 轴 轴就是张量中某一个特定的维度,一个秩等于 1 的张量有一个轴(Axis),一个秩等于 2 的张量有两个轴(Axes)等等。
到目前为止,我们的主要收获是每个index都有一个与之相关的维度;Aijk是一个3x3x3的元素或者组件数组。我们将27个元素很好地安排在我们称之为Rank 3的数组中。Rank 数即indices的数量The rank counts the number of indices。 张量演算的从业者常常把数组元素说成是数字。这其实是一种过度简化。一个数组元素,也被...
Low-rank spectral expansion and tensor hypercontraction are two promising techniques for reducing the size of the two-electron excitation tensor by factorizing it into products of smaller tensors. Both methods can potentially realize an O(r4) quantum chemistry method whereris the number of one-elect...