For introducing a field of science, usually we require a definition which summarizes the goal which is intended to be achieved by this field. Linear Algebra is one of the most important parts of mathematics which has not only interesting pure mathematical ideas but also a lot of applications in physics and engineering. So it seems reasonable to have a Complete, Clear, Brief, and Delicate definition for this important branch of mathematics.
I am wondering that what is the best fit for such a definition. For example, the very first sentence that the Linear Algebra Done Right by Sheldon Axler starts with is
Linear Algebra is the study of linear maps on finite dimensional vector spaces.
What is your definition of Linear Algebra in few sentences?