Eigenvalues and Eigenvectors in Real Life

Eigenvalues and Eigenvectors in Real Life
How eigenvectors and eigenvalues are used outside of the classroom, whether it is on the job or in scientific research. What are some typical real world situations where you find eigenvalues and eigenvectors being used? Pick one such situation and describe it in some detail. Is this application more common in business, science, or engineering? Is it a practical application, or more useful in doing scientific research? What was the most interesting – or useful – thing you learned about how eigenvalues and eigenvectors are used?

Be sure to pick a situation to discuss that nobody else has explored in depth yet. Put the application you chose to explore in depth in the subject line heading of your initial post (for example, “Eigenvalues in quantum mechanics”).
Create an original math homework-type example as it applies to a particular situation, and even work out the numbers, but not do any internet research. Note, however, that the intent of this forum is to do outside research each week and find an application online that you were unfamiliar with, then describe that application in your post. So you will always have outside sources to cite.

Our textbook in section 5.6 contains a number of specific examples and homework problems to give you ideas, both in the e-book and in MyMathLab. You can also search online to find eigenvalue and eigenvector applications and examples. Some good websites to start out with are listed below (but there are many, many others online, so please don’t limit yourself to these):

http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

https://controls.engin.umich.edu/wiki/index.php/EigenvaluesEigenvectors

https://www.khanacademy.org/math/linear-algebra/alternate_bases/eigen_everything/v/linear-algebra—showing-that-an-eigenbasis-makes-for-good-coordinate-systems

http://web.mst.edu/~insall/Student_Corner/Undergraduate%20Students/Linear%20Algebra/Spring%202003/Christy%20Deken/Eigenvalues%20and%20Eigenvectors2.pdf

http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-21-eigenvalues-and-eigenvectors/

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