The Motzkin–Taussky theorem is a result from operator and matrix theory about the representation of a sum of two bounded, linear operators (resp.
The theorem was proven by Theodore Motzkin and Olga Taussky-Todd.
[1] The theorem is used in perturbation theory, where e.g. operators of the form are examined.
be a finite-dimensional complex vector space.
be such that all linear combinations are diagonalizable for all
are of the form (i.e. they are linear in
are independent of the choice of
stands for an eigenvalue of