A linear transformation is a special type of function that takes a vector from one space and transforms it into another vector in a way that preserves the operations of addition and scalar multiplication. This means if you have two vectors, their sum will be transformed in the same way as if you transformed each vector individually and then added the results. In simpler terms, think of a linear transformation as a machine that stretches, shrinks, or rotates vectors without changing their fundamental properties. Common examples of linear transformations include rotation matrices and scaling matrices, which are used in various fields like computer graphics and engineering.