Rank factorization

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, given a <a href="/facts/Field_(mathematics)/xAjAS4ko">field</a> 
 
 
 
 
 F
 
 
 
 {\displaystyle \mathbb {F} }
 
, non-negative integers 
 
 
 
 m
 ,
 n
 
 
 {\displaystyle m,n}
 
, and a <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> 
 
 
 
 A
 ∈
 
 
 F
 
 
 m
 ×
 n
 
 
 
 
 {\displaystyle A\in \mathbb {F} ^{m\times n}}
 
, a rank decomposition or rank factorization of A is a <a href="/facts/Factorization/tXrBXFh1">factorization</a> of A of the form A = CF, where 
 
 
 
 C
 ∈
 
 
 F
 
 
 m
 ×
 r
 
 
 
 
 {\displaystyle C\in \mathbb {F} ^{m\times r}}
 
 and 
 
 
 
 F
 ∈
 
 
 F
 
 
 r
 ×
 n
 
 
 
 
 {\displaystyle F\in \mathbb {F} ^{r\times n}}
 
, where 
 
 
 
 r
 =
 rank
 ⁡
 A
 
 
 {\displaystyle r=\operatorname {rank} A}
 
 is the <a href="/facts/Rank_(linear_algebra)/Yp9b5LK3">rank</a> of 
 
 
 
 A
 
 
 {\displaystyle A}
 
.

Rank factorization open-in-new

Rank factorization