Prove that every element is the sum of two pure tensors ., where .
Thanks in advance.
you're sure that two is not three then? the reason for asking this is that, in general, for any 2-dimensional vector space over a field the "maximum rank" of is 3 and not 2, i.e. every
Thks, but the question requires 2, not 3. They give some hints that consider as a linear map from to (group of 2x2 matrices) (WHY? and HOW?P) and consider two possibilities of the dimension of the image (1 or 2). But I really dont get it.