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

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)

• Maximization of what of a matrix? – tilper Nov 11 '16 at 17:34
• Sorry I thought that the formula was self-explicative. I would like to have a vertical vector where each position i^th of this vector is the highest value of the i^th row of the matrix – Sam Nov 11 '16 at 17:46
• It would be helpful to Readers to have the explanation of your notion of "maximization of a Matrix" added to the body of your Question. You may have thought "the formula was self-explicative" but your concept is closer to an "arg max" than it is to a maximum value. – hardmath Nov 11 '16 at 17:55
• okay, by the way, do you know a better way to denote such operation? – Sam Nov 11 '16 at 18:02
• do you think now the question is clearer? – Sam Nov 11 '16 at 18:05