Every tensor is associated with a linear map that produces a scalar. For instance, a vector can be identified with a map that takes in another vector (in the presence of an inner product) and produces …

Jan 26, 2025 · A tensor itself is a linear combination of let’s say generic tensors of the form . In the case of one doesn’t speak of tensors, but of vectors instead, although strictly speaking they would be …

This is a beginner's question on what exactly is a tensor product, in laymen's term, for a beginner who has just learned basic group theory and basic ring theory. I do understand from wikipedia th...

Sep 20, 2020 · A second-order tensor is comprised at least of a two-dimensional matrix, as an nth-order tensor is comprised at least of an n-dimensional matrix, but what else is in the formal definition. A …

A tensor field has to do with the notion of a tensor varying from point to point . A scalar is a tensor of order or rank zero , and a scalar field is a tensor field of order zero .

May 10, 2007 · Hello Gals, I know what a scalar is. I know what a vector is. I know what a linear transformation is. But what in the name of sweet aunt petunia is a rank 3 tensor? Love, Plx Mny

The meaning of the dot product of two vectors has been well explained below: What does the dot product of two vectors represent? What is physical interpretation of dot product? [duplicate] But, what …

Apr 26, 2012 · Given a metric tensor gmn, how to calculate the inverse of it, gmn. For example, the metric g_ {\mu \nu }= \left [ \begin {array} {cccc} f & 0 & 0 & -w \\...

tensor - In new latin tensor means "that which stretches". The mathematical object is so named because an early application of tensors was the study of materials stretching under tension.

Sep 7, 2008 · From Carroll's textbook: 1. The problem statement Imagine we have a tensor X^ {\mu \nu} with components X^ {\mu \nu} = \begin {pmatrix} 2 & 0 & 1 & -1\\ -1 &...