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)