Linear transformations

A linear transformation is a mathematical function that changes a space or shape in a predictable way, such as stretching, shrinking, or rotating, while preserving the structure of the space. Specifically, it treats additions and scalar multiplications consistently, meaning the transformation of a combination of points equals the combination of their transformations. In practical terms, it's like applying a consistent rule to reshape or reposition objects without distortion or breaking their fundamental relationships, often represented using matrices in coordinate spaces for easier calculations.