##  [Tensor Product](/tensor-product) 

  ##  [Tensor Product](https://quantummech.quantumdictionary.io/tensor-product-0) 

  

 [![Quantum Mechanics Dictionary](/sites/default/files/styles/large/public/2026-01/Quantum%20Mechanics.png.webp?itok=tC_FGCW0)](/topic-specific-dictionaries/modern-physics/quantum-mechanics)

- Modern Physics -

**Quantum Mechanics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A mathematical structure used to represent quantum states and the operations performed on them. It specifies how states are expressed, related, combined, and decomposed into components that support calculation. It does not by itself determine physical predictions without a mapping to observables and measurement rules.



 

 

 

 

 





 

 



 ##  [Tensor Product](https://puremath.quantumdictionary.io/tensor-product-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A universal bilinear construction that, given two modules or vector spaces over a common ring or field, produces a new object whose linear maps correspond exactly to bilinear maps out of the Cartesian product of the factors.

 

 

 

 

 





 

 



 ##  [Tensor Product](https://algebra.quantumdictionary.io/tensor-product-2) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A bilinear construction that, given two modules or vector spaces over a common ring or field, produces a new module or vector space whose linear maps correspond precisely to bilinear maps out of the pair; elements are finite sums of simple tensors v ⊗ w.