Why can I not write every $N \times M$ matrix as multiplication of an $N \times 1$ and a $1 \times M$ matrix?

Question

My intuition says I simply can't express $N \times M$ independent variables in terms of $N+M$ variables but how can I show that?

score 1 · Accepted Answer · answered Aug 27 '14 at 08:19

1

answered Aug 27 '14 at 08:19

user153012

2

Or, just use the fact that $\textrm{rank } (AB) \leq \min{\textrm{rank } A, \textrm{rank } B}$, which could be proved with this decomposition. – Travis Willse Aug 27 '14 at 08:20

1 Answers1