Un-skewing a skew symmetric matrix (for want of a better phrase)

[Trying2Learn]

TL;DR Summary

A better term for the process of creating a skew symmetric matrix

Hello

Say I have a column of components

v = (x, y, z).

I can create a skew symmetric matrix:

M = [0, -z, y; z, 0; -x; -y, x, 0]

I can also go the other way and convert the skew symmetric matrix into a column of components.

Silly question now...

I have, in the past, referred to this as "skewing a column into a skew symmetric matrix" or "unskewing the skew symmetric matrix."

Is there a better phrase to describe this? (mostly, the second one).

(And forget the algebra and the reasons... I just need the term that best describes the process.)

 

[Twigg]

Representing a skew symmetric 3x3 matrix by a vector in $\mathbb{R}^3$ would be the fancy way of saying it.