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pigeons trolling in bus terminal
litsky
65 views
kawaii or kowai?
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Multilinear algebra #10: Algebras
litsky
648 views
Basis of a tensor product. Introduction to algebras (over a field -- a special case of an "algebra over a ring", which is a similar enrichment of the notion of a "module").
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Algebras
litsky
54 views
A different lecture I did on algebras. There are a few careless mistakes that might cause confusion... but I figured it might be helpful to someone anyway.
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Multilinear algebra #9: Tensor product of internal direct sums
litsky
410 views
When V and W decompose directly, so too does their tensor product.
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Multilinear algebra #8: Tensor product of external direct sums
litsky
235 views
Pretty busy these days, but here's a proof that tensor products are chill with respect to direct sums.
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Multilinear algebra #7: Tensor product of subspaces and quotient spaces
litsky
995 views
I first present some observations (which you may like to prove as an exercise), and then go on to talk about the behaviour of the tensor product on subspaces and quotient s...
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Multilinear algebra #6: Induced linear maps
litsky
305 views
Whenever we have a bilinear map phi from VxW to some space Z, we get an induced linear map f, due to the universal property of the tensor product. In this video I talk abou...
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Multilinear algebra #5: More on tensor products
litsky
274 views
The (natural) isomorphisms between the function spaces Hom( V \otimes W, Z ) and Billin( V x W, Z ), and between V \otimes W and W \otimes V (commutativity).
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Multilinear algebra #4: Construction of the tensor product
litsky
561 views
By taking a quotient of the free vector space on the set V x W, I obtain a space T which I then prove satisfies the universal property, hence proving existence of the tenso...
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Multilinear algebra #3: Elementary properties of the tensor product
litsky
367 views
I prove some elementary properties of the tensor product, directly from the definition.
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