What are eigenvalues and why are they useful? скачать в хорошем качестве

What are eigenvalues and why are they useful?

In this video, we begin exploring eigenvalues. We define the standard eigenvalue problem, the general eigenvalue problem, and the quadratic eigenvalue problem. We discuss a long list of applications of the eigenvalue problem including mechanical vibrations problems, electric circuit analysis, image compression, machine learning, data analysis, principal component analysis, the Google Matrix, and finite element analysis. We also discuss my approach to learning: focus on a “keystone” application: an applied problem that sets the foundations upon which many more advanced problems can be built. Our keystone application will be the study of a system of coupled pendula.