# Definition of a tensor

1. Apr 6, 2013

### subsonicman

which said the definition of a tensor was a relation between two vectors. I then went down to the examples section and it had some sort of (n,m) notation. I had some theories on what they meant but none of them made sense. What do n and m represent?

2. Apr 6, 2013

### WannabeNewton

$n$ is just the number of products of $V^{*}$ and $m$ is the number of products of $V$ which comprise the domain of the map; the codomain is just the reals.

3. Apr 7, 2013

### HomogenousCow

That is hardly true, a tensor is a linear object which maps n vectors and m one-forms into real numbers, and transforms in a coordinate invariant manner.
That is like saying multiplication is defined as a relation between two numbers.