Coordinate transformations are mathematical operations that change the way we describe the position of points in space. They allow us to convert coordinates from one system to another, such as from Cartesian coordinates (using x, y, z) to polar coordinates (using r, θ). This is useful in various fields, including physics and engineering, where different perspectives can simplify problems. These transformations can be linear or nonlinear, depending on the relationship between the original and new coordinates. Common examples include rotation, scaling, and translation. Understanding these transformations helps in visualizing and solving complex problems in multiple dimensions.