Talk:Rank factorization

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

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

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

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

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