What is the identity of a linear transformation?

Two important examples of linear transformations are the zero transformation and the identity transformation. It can be demonstrated that, if a transformation is defined by formulas in the coordinates as in the previous example, then the transformation is linear if and only if each coordinate is a linear expression in the variables without a constant term. In this next example, we will see that the identity matrix is the identity transformation matrix. When deciding if a T transformation is linear, generally the first thing to do is to check if T (0) %3D0; if not, T is not automatically linear.