Tensor Preliminaries

Tensors are multidimensional arrays generalized from vectors and matrices, which have a broad range of applications in various fields such as signal processing, machine learning, statistics, dynamical systems, numerical linear algebra, computer vision, neuroscience, network science, and elsewhere. Given the widespread use of tensors, understanding tensor algebra is therefore essential when working with them. Tensor algebra encompasses a wide range of topics as linear algebra, including tensor products, tensor unfoldings, block tensors, tensor eigenvalues, and tensor decompositions, each of which plays a critical role in diverse applications.