Linear operator

A linear operator is a mathematical function that transforms a vector (like a point or a shape in space) into another vector in a way that preserves certain properties. Specifically, it respects addition and scalar multiplication, meaning the transformation of a sum of vectors equals the sum of their transformations, and scaling a vector before or after the transformation yields the same result. These operators are fundamental in areas like computer graphics, physics, and engineering, allowing consistent and predictable changes such as rotations, stretches, or shifts within a space.