Some applications of tensor algebra to estimation theory

Tensor algebra and tensor calculus are widely used in the the fields of mathematics and physics but their usefulness in estimation theory has not been widely appreciated. In this paper we give a short introduction to tensor algebra and provide a few examples of how to use it. None of the results presented in this paper are original but they are novel in showing how tensor algebra can be used to derive results that take much longer and are more cumbersome using a traditional linear algebra approach.