Matrix Representation of Tensors?

[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.

 

[George Jones]

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.

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,

https://www.physicsforums.com/showthread.php?p=874061&#post874061

but this might not have enough detail.

 

[Reedeegi]

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,

https://www.physicsforums.com/showthread.php?p=874061&#post874061

but this might not have enough detail.

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

 

[George Jones]

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

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).

 

[Reedeegi]

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).

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