Eigenvalue Problem
The linear algebra problem of finding non-zero eigenvectors v that, when operated on by a linear operator Â, yield a scalar multiple λ of themselves.
Governing formula
 v = λ v, det(A - λ I) = 0
SI unit
Eigenvalues λ (Scalar Units)
In depth
In physics, eigenvalues represent measurable physical observables (energy, momentum, vibration frequencies). Solving characteristic polynomial det(A - λ I) = 0 yields the system's normal modes and quantum spectrum.
Examples in the real world
Solving the time-independent Schrödinger equation Ĥ ψ = E ψ where energy eigenvalues E represent measurable atomic energy states.