What is a Tensor? - Get Help Here

  • Context: Undergrad 
  • Thread starter Thread starter Eswin Paul T
  • Start date Start date
  • Tags Tags
    Tensor
Click For Summary

Discussion Overview

The discussion centers around the concept of tensors, exploring various definitions and approaches to understanding them. Participants seek clarity on the intuitive understanding of tensors, with a focus on both mathematical and physical perspectives.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses difficulty in forming an intuitive understanding of tensors and requests help.
  • Another participant presents two common methods for defining tensors: one as a multilinear function of vectors and covectors, and the other as a generalization that includes all vectors and covectors as tensors.
  • The second method is noted to be more prevalent in pure mathematics, while the first is favored in physics, with a claim that both methods can be shown to be equivalent.
  • A suggestion is made to watch a video for further understanding.
  • A participant requests additional information about the original poster's mathematical background to tailor the explanation appropriately.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single definition of tensors, as multiple definitions and approaches are presented. The discussion remains unresolved regarding which definition may be more suitable for the original poster's understanding.

Contextual Notes

There are limitations in the discussion, such as the lack of information about the original poster's mathematical background and the potential ambiguity in the definitions provided.

Eswin Paul T
Messages
6
Reaction score
0
I have been trying to understand what a tensor is, still I cannot make an intuitive idea about it. I need help.
Thanks in advance.
 
Physics news on Phys.org
There are a number of different ways of defining a tensor, with two ones being most usual.

Method 1: A tensor is a function that takes a specified number of vectors and covectors (aka dual vectors) as input and gives a scalar as output. To be a tensor, the function must be linear in each of its inputs. We call that being 'multilinear'

Method 2: We start by defining all vectors and covectors to be tensors, and then extend that by saying that anything that is a direct product between two items, each of which is either a vector or a covector, is a tensor.

The second method is used more in pure mathematics, while the first is used more in physics. The two can be shown to be equivalent.

You can think of them as a bit like generalisations of vectors if you like.

If you don't know the bolded words, Wikipedia has quite good explanations of them.
 
  • Like
Likes   Reactions: Eswin Paul T
Try out this video:
 
  • Like
Likes   Reactions: Eswin Paul T
Eswin Paul T said:
I have been trying to understand what a tensor is, still I cannot make an intuitive idea about it. I need help.
Thanks in advance.
You give no information on your mathematical background in your PF profile. What is your background and what experience do you have with vectors? Do you know what unit vectors are? It is very hard to give you an answer on your level without knowing such information.
 
  • Like
Likes   Reactions: Eswin Paul T

Similar threads

Undergrad Understanding Tensors & Knot Theory in Physics
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad What Are Higher Rank Tensors and When Should You Use Matrices in Physics?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Vector and Scalar Tensor Invariance
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why is stress considered a tensor?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Definition of inertia tensor from a differential geometry viewpoint
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Is the Cauchy stress tensor really a tensor?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad What is the row and column expression for the tensor product in index notation?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Is the Lie derivative a tensor itself?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Understanding the stress-energy tensor
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How do Tensors "work" in relation to linear algebraic objects?
  • · Replies 7 ·
Replies
7
Views
1K