Absolute value of all values in a matrix

Question

How do I express the matlab function abs(M), on a matrix $M$, in mathematical terms?

I thought about norms or just $|M|$, but these return scalars, not another matrix of the same size as $M$.

Sorry for the rough explanation, english isn't my primary language.

Answer 1

I think you can also denote the matrix M by giving its generic (i, j)-entry with parenthesis around:

M = (m_ij).

So Matlab's "abs(M)" would simply be: (|m_ij|).

Answer 2

'help abs' returns ABS(X) is the absolute value of the elements of X.

If $ M = [a _{ij}] $ where $a _{ij} \in R$, $i=1...m$ , $j=1..n$ Then $ABS(M) = [ABS(a _{ij})]$

Note: it's not a must for $a _{ij} \in R$ and can be also complex.