See tensor product on Wiktionary
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"ref": "2004, David S. Dummit with Richard M. Foote, chapter 11, in Abstract Algebra, →OCLC, page 421",
"text": "Linear Transformations on Tensor Products of Vector Spaces\n…\nProposition 16. Let V and W be finite dimensional vector spaces over the field F with bases v_1,...,v_n and w_1,...,w_m respectively. Then V⊗_FW is a vector space over F of dimension nm with basis v_i⊗w_j, 1<i<n and 1<j<m.",
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"ref": "2012, 27:30 from the start, in Lecture 1 . Hopf Algebras and Combinatorics (Federico Ardila), spoken by Federico Ardila (Federico Ardila), Federico Ardila, via YouTube",
"text": "[The tensor product] U⊗V is the span of u⊗v:u∈U,v∈V\nmodulo the relations\n·u⊗(v+v')=u⊗v+u⊗v'\\·(u+u')⊗v=u⊗v+u'⊗v\\·(λu)⊗v=λ(u⊗v)=u⊗(λv)",
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-01 from the enwiktionary dump dated 2024-11-21 using wiktextract (95d2be1 and 64224ec). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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