Theory and Computation of Tensors: Multi-Dimensional Arrays

Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships.

Provides an introduction of recent results about tensorsInvestigates theories and computations of tensors to broaden perspectives on matricesDiscusses how to extend numerical linear algebra to numerical multi-linear algebraOffers examples of how researchers and students can engage in research and the applications of tensors and multi-dimensional arrays

1. Introduction and Preliminaries

2. Hankel Tensors

3. Generalized Tensor Eigenvalue Problems

4. M-Tensors and Multi-Linear Equations 5. Tensor Logarithmic Norms 6. Multi-Linear Discriminant Analysis