# Mathematical notation: sorting nonzero elements in a matrix

I have a set $X = \{X_1,\ldots,X_n\}$ where $X_i = [x_1,\ldots,x_m]$ and $x_k$ can be any positive integer value including zero.

I want another set $Y$ such that only the values of $X$ that are greater than zero are included. I was wondering if there is a mathematical notation for this.

For example, let $X_i \in X = [2, 0, 0, 1, 0, 3, 0]$. I want a notation to say that $Y_i \in Y = [2, 1, 3]$ in that order.

Is it correct to say $Y = (X > 0)$ ??, is there a better way to state ?

• Or $y_i=\max[x_i, 0]$. Jul 22, 2022 at 0:37

The notation $Y = (X > 0)$ is conceptually flawed, as you are not selecting the $X_i$ that are "positive" (this is not defined), but applying to every $X_i$ a reduction operation. $Y=\{ (X_1)_{>0},(X_2)_{>0},\cdots(X_n)_{>0}\}$ or $Y=\{ [X_1]_{>0},[X_2]_{>0},\cdots[X_n]_{>0}\}$ could be better.
Borrowing operators from the APL language, you could depict a compression with a selector of positive values, as $(X_i>0)/X_i$.
Other possibility: $X_i|_{>0}$.