##  [Seminorm](/seminorm) 

  ##  [Seminorm](https://natural.quantumdictionary.io/seminorm-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A function p: V → [0,∞) on a vector space V that is positively homogeneous (p(αv)=|α| p(v) for scalars α) and subadditive (p(v+w) ≤ p(v)+p(w)); unlike a norm, p(v)=0 may hold for some nonzero v.

 

 

 

 

 





 

 



 ##  [Seminorm](https://puremath.quantumdictionary.io/seminorm-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 seminorm p on a vector space is a nonnegative functional satisfying absolute homogeneity p(αv)=|α|p(v) and subadditivity p(u+v)≤p(u)+p(v), but it may vanish on nonzero vectors (its kernel can be nontrivial), so positive definiteness can fail.