In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space or manifold) or of the physical space.

Vectors are simple and well-known examples of tensors, but there is much more to tensor theory than vectors. The second chapter discusses tensor fields and curvilinear coordinates. It is this …

It immediately follows that a scalar field is a zeroth-order tensor field, and a vector field is a first-order tensor field. Most tensor fields encountered in physics are smoothly varying and …

What is the difference between a tensor and tensor field? Usually, a tensor field of a manifold $M$ is an assignment of a tensor to each point of $M$. Just like a vector field of $M$ gives you a …

Jun 13, 2025 · Tensor fields are a fundamental concept in field theory, playing a crucial role in describing various physical phenomena in physics and engineering. In this article, we will …

Compute the transformation rules for each of the following, and hence decide whether or not they are tensors. Sub-and superscripted quantities (other than coordinates) are understood to be …

* Tensors and physical theories: A commonplace attributed to Kretschmann states that any local physical theory can be represented in arbitrary coordinates using tensor calculus, but this may …

Introduction to tensor fields. The number flux 4-vector, and its use in defining a conservation law. Instructor: Prof. Scott Hughes. MIT OpenCourseWare is a web based publication of virtually all …

A tensor bundle is built by attaching the associated tensor product vector space to each point of the manifold. Tensor fields are obtained as sections of the tensor bundle.

The stresses inside a solid body or fluid [28] are described by a tensor field. The stress tensor and strain tensor are both second-order tensor fields, and are related in a general linear elastic …