  A matrix $A\in \mathbb{R}^{m \times n}$ is strictly sign regular/SSR (or sign
regular/SR) if for each $1 \leq k \leq \min \{ m, n \}$, all $k\times k$ minors
of $A$ (or non-zero $k\times k$ minors of $A$) have the same sign. This class
of matrices contains the totally positive matrices, and was first studied by
Schoenberg (1930) to characterize Variation Diminution (VD), a fundamental
property in total positivity theory. In this note, we classify all surjective
linear mappings $\mathcal{L}:\mathbb{R}^{m\times n}\to\mathbb{R}^{m\times n}$
that preserve: (i) sign regularity and (ii) sign regularity with a given sign
pattern, as well as (iii) strict versions of these.
