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Minicourse: Matrix Analysis, Spectral Theory. Profs. Anna Skripka and Maxim Zinchenko. Matrix analysis and, in particular, spectral theory are widely used in many areas of mathematics and its applications to other sciences. Introductory ideas of spectral theory (eigenvalues and eigenvectors) first appear in Linear Algebra and Differential Equations. They will serve as an entry point for our minicourse. We will explore these ideas in a more general context of matrix analysis and differential operators. We will start with discussion of spectral theory for finite matrices and its applications to differential equations, problems of classical mechanics, and Markov processes. We will also consider perturbation problems, making an introduction to one of the proposed REU projects. Then we will extend ideas of finite dimensional spectral theory to infinite dimensional setting and discuss its applications to partial differential equations of mathematical physics.
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