What, no category theory
What's really going on is: Take a vector space V and let sigma be the flip operator on V \tensor V: sigma(x \tensor y) = y \tensor x Then we call the +1 eigenspace of sigma the symmetric product and the -1 eigenspace the external product.
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*consults wiki, having gotten lost at “eigenspace”*
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I must have known this once: “The set of all eigenvectors of T corresponding to the same eigenvalue, together with the zero vector, is called an eigenspace or characteristic space of T.”
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So by -1 eigenspace, we mean the elements that just go backward after transformation? And +1 are those unaffected?
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.