Notation: What is the element-wise max notation?

For example I have 3 vectors.

$A_1 = (1, 3, 2, 6)$

$A_2 = (6, 1, 9, 1)$

$A_3 = (3, 8, 4, 0)$

$max A_1 = 6$, $max A_2 = 9$, $max A_3 = 8$

What is the proper max notation for element-wise situation?

like:

$MAX(\mathbb{A}) = (6, 8, 9, 6)$

1 Answer

Let a matrix $A=(A_{ik})_{1\leq i\leq m, \>{1\leq k\leq n}}$ be given. Then we take the max of each column and form the $(n\times 1)$-vector $p$ defined by $$p_k:=\max_{1\leq i\leq m}A_{ik}\ .$$