Application of invertible matrices/inverses, subspaces and/or linear transformations in Mechanical Engineering.

Find of the most interesting (in your opinion) application of invertible matrices/inverses, subspaces and/or linear transformations in Mechanical Engineering. Write 1/2 page to 1 page explaining the following: 1. What concept is used; 2. Where it is used; 3. How and why it is used.