Article writing: How to represent a matrix by its elements?

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Intuitively I guess that parantheses with subscript and superscripts is a way of representing a matrix or an array by its elements, e.g.,

$$ A = (a_{i,j})_{i,j=1}^n $$ (This is taken from here)

However, I can't use this representation in my papers because I am not sure and confident about it. Could you explain or give a reference site?