论文标题
短算法不存在$ 3
Non-existence of a short algorithm for multiplication of $3\times3$ matrices with group $S_4\times S_3$
论文作者
论文摘要
寻找新的矩阵乘法快速算法的前瞻性方法之一是研究接受非平凡对称性的算法。在工作中，研究了乘以$ 3 \ times3 $矩阵的乘法算法，并接受了某个组$ g $同构为$ s_4 \ times s_3 $。结果表明，没有长度$ \ leq23 $的算法。 In the first part of the work, which is the content of the present article, we describe all orbits of length $\leq23$ of $G$ on the set of decomposable tensors in the space $M\otimes M\otimes M$, where $M=M_3({\mathbb C})$ is the space of complex $3\times3$ matrices.在工作的第二部分中，该描述将用于证明与上述组的简短算法不存在。
One of prospective ways to find new fast algorithms of matrix multiplication is to study algorithms admitting nontrivial symmetries. In the work possible algorithms for multiplication of $3\times3$ matrices, admitting a certain group $G$ isomorphic to $S_4\times S_3$, are investigated. It is shown that there exist no such algorithms of length $\leq23$. In the first part of the work, which is the content of the present article, we describe all orbits of length $\leq23$ of $G$ on the set of decomposable tensors in the space $M\otimes M\otimes M$, where $M=M_3({\mathbb C})$ is the space of complex $3\times3$ matrices. In the second part of the work this description will be used to prove that a short algorithm with the above-mentioned group does not exist.
