Geodesic
Generalized Matrices
Canadian journal of mathematics, Tome 41 (1989) no. 3, pp. 556-576

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Similar to the multiplication of square matrices one can definemultiplications for three dimensional matrices, i.e., for the "cubes" of the vectorspace where I denotes a finite set of indices and Kis any field. The multiplications shall imitate the matrix multiplication: To obtain the coefficient γxyzof the product (γxyz) — (αxyz)( βxyz),all coefficients axij, ij∈ I, of the horizontal plane with index xof (αxyz)are multiplied with certain coefficients βhgzof the vertical plane with index z of (βxyz)and the results are added: 
Roesler, Friedrich. Generalized Matrices. Canadian journal of mathematics, Tome 41 (1989) no. 3, pp. 556-576. doi: 10.4153/CJM-1989-024-5
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