learningstill
Jul23-08, 05:28 PM
I've been tasked with proving the existence of a full rank factorization for an arbitrary m x n matrix, namely:
Let \textit{A} \in \textbf{R}^{m x n} with \textit{rank(A) = r} then there exist matrices \textit{B} \in \textbf{R}^{m x r} and \textit{C} \in \textbf{R}^{r x n} such that \textit{A = BC}. Furthermore \textit{rank(A) = rank(B) = r}.
I think I can prove the second property if I assume the first using \it{rank(AB)} \leq \it{rank(A)} and \it{rank(AB)} \leq \it{rank(B)}.
I'd appreciate a push in the right direction. Thanks.
EDIT: I just realized I posted this in the wrong forum. Could a mod move this? My apologies.
Let \textit{A} \in \textbf{R}^{m x n} with \textit{rank(A) = r} then there exist matrices \textit{B} \in \textbf{R}^{m x r} and \textit{C} \in \textbf{R}^{r x n} such that \textit{A = BC}. Furthermore \textit{rank(A) = rank(B) = r}.
I think I can prove the second property if I assume the first using \it{rank(AB)} \leq \it{rank(A)} and \it{rank(AB)} \leq \it{rank(B)}.
I'd appreciate a push in the right direction. Thanks.
EDIT: I just realized I posted this in the wrong forum. Could a mod move this? My apologies.