Consider a hyperplane $\{x\in\mathbb{R}^n|a^Tx=b\}$, and a matrix $M\in\mathbb{R}^{n\times n}$.
For all $x$, we make a transformation $y=Mx$, and I would like to obtain the image of the hyperplane under this transformation in the form of equality constraints.
If $M$ is invertible, the transformed hyperplane is $\{y\in\mathbb{R}^n|a^TM^{-1}y=b\}$.
Is there an algorithmic way to compute the transformed figure for general $M$, including the case where $M$ is singular?