Many of you have seen the announcements on social media that a group of physicists who were studying the behavior of neutrinos had discovered a formula allowing them to compute the eigenvectors of a Hermitian matrix, knowing only the eigenvalues of the matrix and of its principal submatrices. They contacted a prominent mathematician who apparently quickly furnished a proof of their formula. In this talk we shall discuss the formula, illustrate it, and discuss a proof published in an arxiv paper by this team.
This talk is accessible to anyone with some familiarity of the material covered in a first course in linear algebra.