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 …

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 …

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 .

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 …

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 …

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] …

Apr 26, 2014 · The discussion clarifies the distinction between a metric, a metric tensor, and a distance function. A metric is a distance function defined on a metric space, while a metric …

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 10, 2010 · The title says it all, basically I'm trying to figure out what the difference is between the two tensors (levi-civita) that are 3rd rank. Do they expand out in matrix form differently?