How can I write in a compact way $v_j = \max_i Q_{i,j}$ without using indexes?

39 Views Asked by At

Let $Q$ be a matrix. I would like to write in a compact way (without indexing) $$\max_i Q_{*,i}$$ that should return a vertical vector $$v_j = \max_i Q_{j,i}$$

I need it because I have

$$Q = R + \gamma P \max_i Q_{*,i}$$

and I would like to have a matrix notation where there are no indexes. Now in my document I wrote something like

$$Q = R + \gamma P Q^*$$

making clear that $Q^* = \max_i Q_{*,i}$. But, if I find a more appropriate way to write this "operator" it will be great! (Q is a matrix, R is a matrix, P is a 3-d matrix)