##  [Singular Value](/singular-value) 

  ##  [Singular Value](https://natural.quantumdictionary.io/singular-value-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 nonnegative scalar σ associated with a linear map that quantifies how much the map stretches or compresses vectors in specific orthogonal directions; for a real matrix A, σ is a square root of a nonnegative eigenvalue of A^T A.

 

 

 

 

 





 

 



 ##  [Singular Value](https://algebra.quantumdictionary.io/singular-value-1) 

  

 [![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 nonnegative scalar equal to the square root of an eigenvalue of A*A^* (or A^*A) for a matrix A, representing the magnitude by which A stretches or compresses unit vectors along orthogonal directions.