Square matrix notation (orthogonal superscript)

Question

I am reading a paper and have a question about notation that I am not familiar with. The expression I need help with is given below. I am unfamiliar with orthogonal superscript following a square matrix.

$$ y = A^{\perp}Bx $$ where $ A \in \mathbb{R}^{\text{m} \times \text{m}}, \ B \in \mathbb{R}^{\text{m} \times \text{n}}, \ x \in \mathbb{R}^{\text{n}}, \ y \in \mathbb{R}^{\text{m}} $

Is $ A^{\perp} $ simply any square matrix (excluding the trivial zero matrix) orthogonal to $A$ (i.e. $ A^{\perp}A=[0] \text{, where } [0]$ is the m$\times$m zero matrix)?

Thanks in advance for any help.

Answer 1

The author of the paper has answered my question. The notation is as speculated in the original post. In particular, $A^{\perp}$ is a matrix orthogonal to $A$. In other words $ A^{\perp} $ satisfies the following; $$ A^{\perp}A=0, \ A^{\perp} \neq [0] $$