Eigenvectors and eigenvalues are ubiquitous because they characterize linear transformations: operations that stretch, squeeze, rotate, or otherwise change all parts of an object in the same way.

Outside particle physics, eigenvalues and eigenvectors are used in analyzing vibrating systems and facial recognition programs. Linear algebra is used everywhere in quantitative sciences, engineering ...

They’d noticed that hard-to-compute terms called “eigenvectors,” describing, in this case, the ways that neutrinos propagate through matter, were equal to combinations of terms called “eigenvalues,” ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

When a Hermitian linear operator is slightly perturbed, by how much can its invariant subspaces change? Given some approximations to a cluster of neighboring eigenvalues and to the corresponding ...

This problem is known as order determination, and amounts to estimating the rank of a matrix. Previous order-determination procedures rely either on the decreasing pattern, or elbow, of the ...