# Linear transformation

> A function between vector spaces that preserves their vector addition and scalar multiplication properties, satisfying two conditions: for any vectors $u$ and $v$, and any scalar $c$, the transformation $T$ must follow $T(u + v) = T(u) + T(v)$ and $T(cv) = cT(v)$.

A function between [vector spaces](https://wiki.g15e.com/pages/Vector%20space.txt) that preserves their vector addition and scalar multiplication properties, satisfying two conditions: for any vectors $u$ and $v$, and any scalar $c$, the transformation $T$ must follow $T(u + v) = T(u) + T(v)$ and $T(cv) = cT(v)$.