I have matrix $\textbf{X}$. And I need to denote the vector of mean values of the matrix columns.
Is it correct to use $\bar{\textbf{x}}$? Or Should I use different notation? Or is this notation correct if I use explanation what it means?
What is the most correct approach?
I think it is correct if you introduce that notation. Also note that to be really correct, you should always write something like “let $X, Y$ be some matrices and let $\bar{x}, \bar{y}$ denote the corresponding vectors of means of the columns” any time you consider particual matrices.
On the other hand, if you use notation $\bar{X}$ instead, you may write “$\bar{X}$ denotes the vector of mean values of the columns of any matrix $X$”, and then you can use $\bar{X}, \bar{Y}, \bar{Z}$ without any further explanation.