gen-explain-a-linear-map-as-you-would-to-a-capable-student-in-3-4f55

Explain a linear map as you would to a capable student, in 3-4 sentences.

A linear map is a function between vector spaces that preserves the two fundamental operations: addition and scalar multiplication. This means that if you add two vectors and then apply the function, you get the same result as applying the function first and then adding—and similarly, scaling a vector before or after applying the function gives the same outcome. You can think of linear maps as transformations that keep straight lines straight and the origin fixed, like rotations, reflections, or stretches in space. Once you know where a linear map sends the basis vectors, you can determine where it sends any vector at all.