Linear Transformations

Linear transformations serve as the mechanism by which vectors are mapped from one vector space to another while preserving the operations of addition and scalar multiplication. They are the mathematical equivalent of reshaping, rotating, stretching, or projecting a space countless applications in ML, computer graphics, physics, and engineering. By representing these transformations as matrices, we gain a powerful tool to analyze and compute how inputs are transformed into outputs, whether it’s rotating a 3D model in a video game, compressing data in ML, or solving systems of equations.