This bachelor thesis explores an intriguing connection between ellipses, Blaschke products and matrix theory. It discusses a special type of ellipse that emerges as a geometric consequence of the properties of the third-degree Blaschke product. Furthermore, we analyze how are these ellipses related to the problem of finding
polynomials whose zeros lie on the boundary of the complex unit disc, while their critical points are within the disc. It is also shown that this geometric-analytic problem can be formulated in the language of matrices, which opens the door to generalizations in higher dimensions.
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