$n \times m$ matrix conversion? Is it possible to convert an $n\times m$ matrix $A$ such that
$$ A=CB $$
where $B$ is a $1\times m$ matrix which contains all elements of $A$, and $C$ is a $n\times 1$ matrix. I'm assuming no since this might give a special case of matrices.. but i am not so sure. If this is not possible, is it possible to extend matrix $A$ to ($n$ by $m$) by ($n$ by $m$) so the same conditions are met, yet the matrix is replicated and the result needs to be unique. Just to give a reason for this, i figured out a way to make $A$ into a $1$ by ($n$ by $m$) vector $B$, but to find an inverse of this, i need to solve $A=CB$, which is what's giving me problems. 

Regarding your intial question. No, it isn't be possible:
Consider an nxm matrix of random values - it has n.m independent points of data. Where as a 1xm and a nx1 matrix together have only n+m independent points of data.
There's less data being stored so the two cannot be equivalent.
I don't think I can answer the rest of your question. Sorry.
