linear transformation

A linear transformation is a specific type of function that takes input from one space (like a set of numbers or points) and produces output in another space while preserving certain properties. It maintains straight lines and the origin—meaning if you stretch or shrink a shape, it stays in proportion and aligned. For example, if you imagine stretching or rotating a piece of fabric without tearing it, that's similar to what a linear transformation does with data or geometric figures. It’s essential for understanding changes in mathematics, computer graphics, and physics.