The Geometry of Rank Decompositions of Matrix Multiplication I: 2 x 2 Matrices
The Geometry of Rank Decompositions of Matrix Multiplication I: 2 x 2 Matrices
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DOI：
10.1080/10586458.2017.1403981
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发表时间：
2019-07-03
影响因子：
0.5
通讯作者：
Ottaviani, Giorgio
中科院分区：
文献类型：
--
作者：
Chiantini, Luca;Ikenmeyer, Christian;Ottaviani, Giorgio
这是关于矩阵乘法张量的秩分解的系列论文中的第一篇。在本文中，我们建立了有关张量秩分解的一般事实，描述了搜索新矩阵乘法分解的潜在方法，给出了建立 Strassen 算法对称群的 Burichenko 定理的几何证明，并提出了 Strassen 分解家族中两个特别好的子家族。
This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper, we establish general facts about rank decompositions of tensors, describe potential ways to search for new matrix multiplication decompositions, give a geometric proof of the theorem of Burichenko establishing the symmetry group of Strassen's algorithm, and present two particularly nice subfamilies in the Strassen family of decompositions.