Motzkin-Taussky Theorem

The Motzkin-Taussky theorem, proved by Theodore Motzkin and Olga Taussky-Todd in 1952, is a result in operator and matrix theory describing sums of two bounded linear operators, or equivalently two matrices, that are jointly diagonalizable in the sense that every linear combination of them is itself diagonalizable. Under that condition, the theorem shows the eigenvalues of any linear combination of the two operators must themselves be linear combinations of the two operators' own eigenvalues, a property the original authors called property L, with applications in perturbation theory.