Prove that every element is the sum of two pure tensors ., where .

Thanks in advance.

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- December 6th 2009, 02:32 PMsmith09Tensor
Prove that every element is the sum of two pure tensors ., where .

Thanks in advance. - December 6th 2009, 11:26 PMNonCommAlg
- December 7th 2009, 01:26 AMsmith09
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.

- December 7th 2009, 11:42 AMsmith09
Oh, sorry, here must be in a dense open subset.

- December 15th 2009, 10:24 AMsmith09
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.