In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity theory. In this paper, we characterize existing decompositions (found by any algorithm) by certain vectors called signature, and transform them in another decomposition which can be more suitable in practical algorithms. In particular, we present a novel decomposition of the tensor multiplication of matrices of the size 3x3 with 3x6 with rank 40.

翻译：在本文中,研究了与矩阵乘法相对应的气态分解( CP) 气态聚变( CP) 。 查找这些气态的等级和计算分解( 分解) 是代数复杂理论的一个根本问题 。 在本文中, 我们描述某些矢量( 任何算法) 的分解( 由任何算法所发现 ), 即 签名, 并将其转化成另一种分解, 更适合 实际算法 。 特别是, 我们呈现了一种新型分解, 3x3 和 3x6 的矩阵的分解( 3x3 和 40 级 ) 的分解( 3x6 和 3x6 ) 的分解( 4 级 ) 。