##  [Multilinearization](/multilinearization) 

  ##  [Multilinearization](https://algebra.quantumdictionary.io/multilinearization-0) 

  

 [![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 transformation that replaces a polynomial map or multilinear-unaware function by an explicitly multilinear map that encodes its homogeneous multilinear components (the polarized or polarized-like form). It is used to isolate the k-linear parts of degree-k homogeneous pieces and to represent nonlinear operations as multilinear tensors or symmetric forms.