Tensor Product

Tensor product notation can be used to mathematically model, in terms of matrix factorizations, computations from many diverse fields, including digital signal processing, linear systems, and numerical analysis. Typically, large data sets are processed by algorithms characterized by intricate index calculations. The problem of analyzing and writing code for such algorithms that is tailored to a specific architecture or processor is both time-consuming and error-prone. The formalism of the tensor product notation provides powerful tools for keeping track of these index calculations and for establishing simple rules, in the form of tensor product identities, that can be used to modify an algorithm for optimal performance as data size and target architecture vary. By mapping certain basic tensor product operations onto code or hardware, a large array of algorithms can be implemented by simple algebraic manipulations rather than more timeconsuming programming manipulations.