Talk:Rank factorization

Arbitrary field
Rank factorization holds for arbitrary fields. Thatsme314 (talk) 01:38, 7 September 2022 (UTC)

Definition in leading section
"...given a field $$\mathbb F$$, nonnegative integers $$m,n$$, and a matrix $$A\in\mathbb F^{m\times n}$$, a rank decomposition or rank factorization of $A$ is a factorization of $A$ of the form $A = CF$, where $$C\in\mathbb F^{m\times r}$$ and $$F\in\mathbb F^{r\times n}$$, where $$r=\operatorname{rank} A$$ is the rank of $$A$$."

Doesn't the definition (according to other sources) also require $$C,F$$ to be full rank?

Thatsme314 (talk) 01:48, 7 September 2022 (UTC)


 * The former definition implies the latter by this inequality. Saung Tadashi (talk) 18:08, 16 October 2022 (UTC)