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

Thanks in advance.

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- Dec 6th 2009, 03:32 PMsmith09Tensor
Prove that every element is the sum of two pure tensors ., where .

Thanks in advance. - Dec 7th 2009, 12:26 AMNonCommAlg
- Dec 7th 2009, 02:26 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.

- Dec 7th 2009, 12:42 PMsmith09
Oh, sorry, here must be in a dense open subset.

- Dec 15th 2009, 11:24 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.