Prove that every element is the sum of two pure tensors ., where .
Thanks in advance.
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Originally Posted by smith09 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
element of is a sum of at most 3 simple tensors.
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.
Oh, sorry, here must be in a dense open subset.
Is there any ideal then? I think the first case (1 dim) is not so hard. But the second case is ...not easy.
Thks in advance.
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