Express a linear map in matrix form Is there anyway to express the linear map $x\mapsto (a^Tx)b, \, a,b,x\in\Bbb R^n$ in matrix form $x\mapsto Ax$?
Context: I'm trying to solve an equation in $x\in\Bbb R^n$:
$$ab^Tx-(a^Tx)b=c$$
If I'm able to express $(a^Tx)b$ in martrix form $Ax$ I'm done (we don't need to care about existence or uniqueness of solutions since from other aspects it's guaranteed $(ab^T - A)$ will be invetible. 
Best regards. 

$a^Tx$ is a scalar, hence
$$(a^Tx) b= b(a^Tx)=(ba^T)x$$
