  In past few decades, tensor algebra also known as multi-linear algebra has
been developed and customized as a tool to be used for various engineering
applications. In particular, with the help of a special form of tensor
contracted product, known as the Einstein Product and its properties, many of
the known concepts from Linear Algebra could be extended to a multi-linear
setting. This enables to define the notions of multi-linear system theory where
the input, output signals and the system are multi-domain in nature. This paper
provides an overview of tensor algebra tools which can be seen as an extension
of linear algebra, at the same time highlighting the difference and advantages
that the multi-linear setting brings forth. In particular, the notion of tensor
inversion, tensor singular value and tensor Eigenvalue decomposition using the
Einstein product is explained. In addition, this paper also introduces the
notion of contracted convolution in both discrete and continuous multi-linear
system tensors. Tensor Networks representation of various tensor operations is
also presented. Also, application of tensor tools in developing transceiver
schemes for multi-domain communication systems, with an example of MIMO CDMA
systems, is presented. Thus this paper acts as an entry point tutorial for
graduate students whose research involves multi-domain or multi-modal signals
and systems.
