Selecting diagonal elements from a matrix to make a vector

[MasterD]

Hi,

I am looking for a certain operation that makes a 1 tensor from a 2 tensor by filtering out only the diagonal elements.

For instance,

(f1g1 f1g2 f1g3)
(f2g1 f2g2 f2g3)
(f3g1 f3g2 f3g3)

becomes

(f1g1)
(f2g2)
(f3g3)

after a certain operation.

What operation could I use?

Thanks a million for the one who can help me out here.

Dirk

 

[Ben Niehoff]

I don't think the resulting object is a 1-tensor. How would it transform?

If all you want is the SUM of those elements, then you can do simple tensor contraction: T_iⁱ. To make a 1x3 object out of the diagonal elements, you could write (no summation convention):

$$\sum_i T^{ii} \vec e_i$$

But this object is NOT a vector; it doesn't transform correctly.