Eigenvalue
Definition
A matrix's special scaling numbers — along eigenvector directions, the matrix stretches but doesn't rotate.
Symbol: ·
Technical definition
Av = λv, with λ found from det(A − λI) = 0. In quantum mechanics, the eigenvalues of operators are the measurable values.
Example
Hydrogen's energy levels are eigenvalues of the Hamiltonian operator — 'quantized energies' literally means eigenvalues.
Common confusion
Not every matrix has real eigenvalues — planar rotations have complex ones. 'No eigenvalue' usually means 'no REAL eigenvalue'.