An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion of different matrix expressions is revealed. The various contracted products of hypermatrices are realized by semi-tensor products (STP) of matrices via matrix expressions of hypermatrices.

翻译：本文引入了超矩阵的一种等价定义，并提出了超矩阵的矩阵表示法。利用置换矩阵，揭示了不同矩阵表示之间的转换关系。通过超矩阵的矩阵表示，基于矩阵的半张量积（STP）实现了超矩阵的多种收缩积。