I don't get it, what's cool about it? Einstein notation seems good enough for most of the things and they are equivalent. Is there anything interesting (i.e. new) that this notation allow?
It is much better for working with (a) low-rank approximations and (b) optimizing the order of operations. While (b) is "merely" a question of computational performance, (a) can have extremely important fundamental/theoretical consequences for the problem under study (e.g. finding efficient classical algorithms for modeling quantum mechanics).
