# min max and range of the matrix: How to mathematically write that?

I have two questions about mathematical notation.

1. Let F be the matrix of $i$ rows and $j$ columns. I want to found min and max values of that matrix for every row. Currently, I have this

$$l_i = \min\limits_{j \in \{1, ..., n\}} f_{ij}, \quad i = 1, ..., m,$$ $$u_i = \max\limits_{j \in \{1, ..., n\}} f_{ij}, \quad i = 1, ..., m,$$

Ideally, I would like to write this such that it would result in another matrix with two columns, one of lower bounds and the other one with the upper bounds. How would I write that? Any other suggestions to write this are greatly appreciated. Could you write it like this? $$\textbf{D} = [\min\limits_{j \in \{1, ..., n\}} f_{ij}, \max\limits_{j \in \{1, ..., n\}} f_{ij}], \quad i = 1, ..., m.$$

1. How do you write mathematically the range between two column vectors with $m$ observations? I have this: $$\textbf{Rng} = |\min(\textbf{F}) - \max(\textbf{F}) |$$ Is this okay?
• I haven't read your suggestion for $D$. Even if it's correct I wouldn't use it. Write words instead. Define your lists of lower and upper bounds and then tell your reader to put them in a two column matrix. – Ethan Bolker Feb 21 '18 at 17:49
• Agree with the previous comment. If getting the vector $Rng$ is your ultimate aim, then just write something like "Let $Rng_i$ be the range of values in each row $F_i$ of $F$". – tobwin Feb 21 '18 at 18:20
• Oki that sounds good. thank you! :) – Aureja Zelvyte Feb 21 '18 at 19:35