# I What is a Tensor?

1. Oct 5, 2016

### Eswin Paul T

I have been trying to understand what a tensor is, still I cannot make an intuitive idea about it. I need help.

2. Oct 5, 2016

### andrewkirk

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.

3. Oct 6, 2016

### pixel

Try out this video:

4. Oct 6, 2016

### Staff: Mentor

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.