Matrix Representation of Tensors?

1. Aug 20, 2008

Reedeegi

How would you represent tensors as matrices? I've searched all over, and my book on GR (Wald) only has one example where he makes a matrice from a tensor, and I still don't understand the process.

2. Aug 20, 2008

George Jones

Staff Emeritus
A tensor is a muti-linear mappring. A rank 2 tensor can be turned into a matrix by letting it operate on a basis or dual basis. See,

but this might not have enough detail.

3. Aug 20, 2008

Reedeegi

how often are rank-2 tensors used in GR, by chance?

4. Aug 20, 2008

George Jones

Staff Emeritus
Quite often; the metric tensor, the stress-energy tensor, the Einstein tensor, and the Ricci tensor all examples of rank 2 tensors.

Introducing a basis turns (the components of):

a rank 1 tensor into a column or row of values;

a rank 2 matrix into a square matrix of values;

a rank 3 tensor into a cube with values in each subcubes (think rubik's cube).

5. Aug 20, 2008

Reedeegi

okay, that's what I thought... thanks a lot for your help!