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Diff — Tensor product

Revision #3192 → #3702 · back to history

modifiedTensor product of two vector spacesabc496e326a7
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noteMathlib defines `TensorProduct R M N` for modules over a commutative semiring, which subsumes the vector-space case.Mathlib defines `TensorProduct R M N` for modules over a commutative semiring, subsuming the vector-space case.
modifiedTensor product from bases40ebd6614177
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note`Basis.tensorProduct` builds a basis of `M ⊗ N` from bases of `M` and `N`.`Module.Basis.tensorProduct` builds a basis of `M ⊗ N` from bases of `M` and `N`.
modifiedTensor product of vectors via basis decomposition6738ebc1eb8f
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note`Basis.tensorProduct_apply` describes how `v ⊗ w` expands in the product basis.`Module.Basis.tensorProduct_apply` describes how `v ⊗ w` expands in the product basis.
modifiedSymmetric group action on tensor powers341df49d2c93
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mathlib.moduleMathlib.LinearAlgebra.PiTensorProductMathlib.LinearAlgebra.PiTensorProduct.Basic
modifiedType (r,s) tensora845d2dcb2ee
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mathlib.moduleMathlib.LinearAlgebra.PiTensorProductMathlib.LinearAlgebra.PiTensorProduct.Basic
modifiedHigher Tor functors and derived tensor producte76a737eecea
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mathlib.declTorCategoryTheory.Tor
noteMathlib defines `Tor n : C ⥤ C ⥤ C` in `CategoryTheory.Monoidal.Tor`; a single packaged 'derived tensor product' term is not standard.Mathlib defines `CategoryTheory.Tor n : C ⥤ C ⥤ C` in `CategoryTheory.Monoidal.Tor`; a single packaged 'derived tensor product' term is not standard.
addedMonoidal category as general setting for tensor producta8dcb09d0015
addedTensor product of graphs (categorical product)6b671c2373a8
addedKronecker product of matricesaa7f4b3e390e
addedTensor product distributes over direct sums (graded tensor product)99a5e9ec16b2
addedFree module on a set (Cartesian product basis for L)00ce1c474f36