Matriceje
Matriceje is a concept in multilinear algebra describing a class of multi-dimensional arrays that generalize matrices. A matriceje of order k is an array A with dimensions n1×n2×...×nk whose entries lie in a field. The key operation, the matricial product, generalizes matrix multiplication by performing contractions over shared indices.
Through a prescribed pattern of contractions, two matriceje can be combined to yield a new object whose
Matriceje form an algebra under the matricial product, with an identity object corresponding to a diagonal
In practice, to compute with matriceje, one commonly unfolds (matricizes) the array along a mode to obtain
Applications are found in higher-order data analysis, quantum information, and machine learning, where multi-way interactions are
The term matriceje is etymologically related to matrix plus a Slavic plural suffix, and its use remains