What Is the Eigenvalue Problem and How Do You Solve It?

Rhett Allain
9 min readMay 10, 2024
Photo: Rhett Allain. Angular momentum as an example of the eigenvalue problem

This won’t make sense (yet), but the eigenvalue problem looks like this:

This equation says that a matrix (A) operating on a vector (r) is equal to a scalar (λ) multiplied by the same vector. I actually remember seeing this for the first time and just thinking — “hey, wouldn’t A just be equal to λ?”. Alas, no. A is a matrix and λ is a scalar. They can’t be equal.

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Rhett Allain

Physics faculty, science blogger of all things geek. Technical Consultant for CBS MacGyver and MythBusters. WIRED blogger.