Practical applications of eigenvectors

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Eigenvectors and eigenvalues are essential concepts in linear algebra, often used in various practical applications such as stability analysis, quantum mechanics, and facial recognition technology. The discussion highlights a need for practical examples of eigenvector problems, particularly using a 2x2 matrix. While the theory is understood, there is a challenge in creating a relevant problem that applies these concepts. Resources like Wikipedia can provide foundational knowledge, but specific application scenarios are sought. Exploring real-world contexts can enhance understanding and facilitate problem creation involving eigenvalues and eigenvectors.
Martin III
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Homework Statement


A simple eigenvector problem using a 2x2 matrix.

Homework Equations


Ax = \lambda x

The Attempt at a Solution


I don't have one. I know and understand the theory behind eigenvectors, but I cannot think of a practical application. I need to create a problem that uses eigenvalues/eigenvectors as a solution.
 
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