I'm having a little difficulty doing some basic exercises in the Einstein notation. The exercises in particular are attached to this post.
In exercise 0, I get that, for example, refers to the entry located in row i column j of a change of basis matrix A. To solve the exercise, I first do;
, since T is linear. Now if I understand this correctly, I think;
. Now I get that the next step I must do is write all of these . However i'm having trouble writing the two nested sums with the Einstein notation. Intuitively I just feel like writing; , because for a fixed j, we sum over the i, and for every of these i, we sum over the k. From there However, I don't know what to do with , my indices get very confusing and crazy, and I'm not sure what I can be allowed to simplify or all.
Anyway, I hope all of this is understandable.