Matrix Diagonal Multiplication I have a matrix-vector inner product multiplication $G = X D x$ where $D$ is a diagonal matrix. Now let's say I already know $E = Xx$. Is there a method that I can use to change $E$ into $G$ using $D$ without having to calculate $G$ in full?

Merely knowing the vector $E$ and the matrix $D$ doesn't seem to be enough to determine $G$, since $E$ is some vector in the column space of $X$, and $G$ can be more or less any other vector in that column space. I don't see how you can tell what $G$ is without using what the individual columns in $X$ are and how they were combined to obtain $E$.
