Difference between revisions of "Tensor product"
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{{WikiEntry|key=Tensor Product|qCode=1163016}} is a foundational operator in [[Linear Algebra]]. In mathematics, the tensor product is a vector space to which is associated a [[bilinear map]] V × W → V ⊗ W. | {{WikiEntry|key=Tensor Product|qCode=1163016}} is a foundational operator in [[Linear Algebra]]. In mathematics, the tensor product is a vector space to which is associated a [[bilinear map]] V × W → V ⊗ W. | ||
=Defined Through a Universal Property= | =Defined Through a Universal Property= | ||
The tensor product can also be defined through a [[universal property]]. As for every universal property, all objects that satisfy the property are isomorphic through unique isomorphisms. When this definition is used, the other definitions may be viewed as constructions of objects satisfying the universal property and as proofs that there are objects satisfying the universal property, that is that tensor products exist. | The following statement is an excerpt from Wikipedia: | ||
The tensor product can also be defined through a [[universal property]]. As for every universal property, all objects that satisfy the property are isomorphic through unique isomorphisms. When this definition is used, the other definitions may be viewed as constructions of objects satisfying the universal property and as proofs that there are objects satisfying the universal property, that is that tensor products exist. | |||
[[Category:Linear Algebra]] | [[Category:Linear Algebra]] | ||
[[Category:Tensor Calculus]] | [[Category:Tensor Calculus]] | ||
[[Category:Category Theory]] | [[Category:Category Theory]] | ||
Latest revision as of 13:23, 20 March 2022
Tensor Product(Q1163016) is a foundational operator in Linear Algebra. In mathematics, the tensor product is a vector space to which is associated a bilinear map V × W → V ⊗ W.
Defined Through a Universal Property
The following statement is an excerpt from Wikipedia:
The tensor product can also be defined through a universal property. As for every universal property, all objects that satisfy the property are isomorphic through unique isomorphisms. When this definition is used, the other definitions may be viewed as constructions of objects satisfying the universal property and as proofs that there are objects satisfying the universal property, that is that tensor products exist.