Linear Transformation Theory

Linear transformation theory studies how certain functions reshape space in a consistent way, preserving the basic structure of lines and angles. Essentially, it describes how an entire set of points (like a shape) can be stretched, rotated, sheared, or reflected, while maintaining straight lines and proportional relationships. These transformations can be represented mathematically by matrices, enabling precise calculations of how objects move or change shape. This theory is fundamental in areas like computer graphics, engineering, and physics, as it provides a systematic way to understand and predict how objects behave under various linear changes.