Extract a vector that is in the middle of a matrix equation

Question

So I have the following problem that is giving me a hard time for some reason:

I have a matrix equation of the form $RA(I-\alpha e')$ where

• $R$ is an $n \times n$ matrix
• $A$ is a triangular $n \times n$ matrix
• $I$ is the $n \times n$ identity matrix
• $\alpha$ is a $n \times 1$ vector and
• $e'$ is a $1 \times n$ vector of ones.

Clearly this equation is some linear mapping $f(\alpha)$. I am now wondering if (and if yes how) it is possible to rewrite this equation into the form.

$f(\alpha) = X\alpha$?

I have been thinking and trying and researching but I wasn't able to come up with a good answer.

Thank you! Rob

Answer 1

I don't think so, the second equation you're writing should output a vector (if $X$ is a matrix), while the first equation you're writing should output a matrix. Also the first equation is not linear but affine ($f(v+w)\neq f(v)+f(w)$ for $v,w\in\mathbb{R}^{n\times1}$).