Built upon the principles of diagonalization and superposition, this text contains many important physical applications—such as population growth, normal modes of oscillations, waves, Markov chains, stability analysis, signal processing, and electrostatics—to show students the incredible power of linear algebra in the real world. The underlying ideas of breaking a vector into modes, and of decoupling a complicated system by suitable choice of linear coordinates, are emphasized throughout the book. It impresses upon students the importance of these principles, while giving them enough tools to use them effectively in a variety of settings.