Abstract
If you were to ask a controls engineer why one should care about eigenvalues, the answer would be obvious and immediate. Eigenvalues are absolutely critical to anyone designing controllers or wanting to understand how a system behaves. Eigenvalues can literally tell us whether or not an aircraft will crash, or if an infectious disease will turn into a global pandemic. Now, if you were to ask the same question to a college student early on in their educational journey who has just completed their first course in linear algebra, the answer would more than likely be a blank stare or some semiconfused story about how eigenvalues are these mysterious numbers that somehow connect vectors and matrices (which are probably also somewhat mysterious, by the way). Similar statements can be made about Laplace transforms, imaginary numbers, differential equations, random processes, or a whole slew of similarly important yet initially unclear objects. So why in the world would someone keep taking courses covering these topics, with no obvious endgame in sight, to one day in the distant future become a controls engineer?
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