An index formalism that generalizes the capabilities of matrix notation and algebra to n-way arrays

The capabilities of matrix notation and algebra are generalized to n-way arrays. The resulting language seems easy to use; all the capabilities of matrix notation are retained and most carry over naturally to the n-way context. For example, one can multiply a three-way array times a four-way array to obtain a three-way product. Many of the language's key characteristics are based on the rules of tensor notation and algebra. The most important example of this is probably the incorporation of subscript/index-related information into both the names of array objects and the rules used to operate on them. Some topics that emerge are relatively unexplored, such as inverses of n-way arrays; these might prove interesting for future theoretical study. Copyright (C) 2001 John Wiley & Sons, Ltd.