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The Art of Problem Solving

I need to prepare a talk on tensor algebra, so I am trying to refresh my memory about that... I have a question about the conditions (as explicit as possible) when a tensor A can be decomposed into a product of two tensors of lesser...


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		abstract tensor products of vector spaces
		The Art of Problem Solving
		I'm used to thinking of tensors as multilinear maps on a k-fold direct product of vector spaces into the reals. So suppose we have a tensor T: \underbrace{V\times\ldots\times V}_k\rightarrow R. I want to understand why the space of ...
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		Tensor Products and Bases
		The Unapologetic Mathematician
		Since we’re looking at vector spaces, which are special kinds of modules, we know that has a tensor product structure. Let’s see what this means when we pick bases. First off, let’s remember what the tensor product of two vector ...
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		Antisymmetric Tensors
		The Unapologetic Mathematician
		Let’s continue yesterday’s project by considering antisymmetric tensors today. Remember that we’re starting with a tensor representation of on the tensor power , which also carries an action of the symmetric group by permuting th...
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