Stretching and condensing tensors. Application to tensor and matrix equations

Abstract

Since tensors are vectors, no matter their order and valencies, they can be represented in matrix form and in particular as column matrices of components with respect to their corresponding bases. This consideration allows using all the available tools for vectors and can be extremely advantageous to deal with some interesting problems in linear algebra, as solving tensor linear equations. Once, the tensors have been operated as vectors, they can be returned to their initial notation as tensors. This technique, that is specially useful for implementing computer programs, is illustrated by several examples of applications. In particular, some interesting tensor and matrix equations are solved. Several numerical examples are used to illustrate the proposed methodology.

Computer algebra in gravity research

“…I have been unable to download a copy, though there is a webpage [C45], with a latest date 2007, stating it was updated to Mathematica 6.0. Tensors: This provided tensor facilities based on multilinear algebra and matrix methods (Ruíz-Tolosa and Castillo 2004 ) but the software download page at [C46] still refers to Mathematica 4.0. It appears to have been focused on tensors in Euclidean space.…”