The array matrix generalization for signal processing

The diversity of notation permeating the publications on signal processing suggests the need for some consolidation and standardization. We advocate here the array theory and notation of Tait as a standardizing framework for a smooth transition from the vector-matrix era to the array domain and array processing era. A duality between array domain and matrix domain operations blends the flexibility and power of the array domain with the compactness and overview attributes of matrix expressions. The notation facilitates tractability through the super- and subscript patterns for the indices and the range set of the indices. We introduce fundamentals from Tait´s work with some consolidation and exemplify notation and manipulations. The relevance for signal processing is demonstrated more fully in a companion paper [8].