[Math] Finding the convex hull of m x n matrices

Question

Given a set of $\mathbb{R}^{m \times n}$ matrices, I would like to find the matrices forming the vertices of their convex hull.

Would this be the same problem as finding the convex hull of a set of vectors in $\mathbb{R}^{m + n}$? ie: Could I simply reshape the matrices into vectors and proceed with known algorithms to find the convex hull, and then convert back into $\mathbb{R}^{m \times n}$?

PS: Please be kind. I am a engineer with limited experience in this field. If you could point me to any references that could be helpful, I's appreciate it.

Thanks

Edit:

1. My set of $\mathbb{R}^{m \times n}$ matrices is finite and each matrix is discrete.

2. Some additional clarification: I am building this set up one matrix at a time. Each time I have a new matrix, I want to test if the new matrix is contained within the convex hull formed by the matrices already in the set. If it is, then I can ignore it. If it is not in the convex hull, then I add it to the set and extend the convex hull to include the new matrix.

Answer 1

Since $\mathbb R^{m\times n}$ is isomorphic as a vector space to $\mathbb R^{mn}$ (note that that‘s not a plus) via the obvious map (taking all entries), you can indeed do the computation in $\mathbb R^{mn}$.