  In the present paper we prove that every additive (not necessarily
homogenous) local inner derivation on the algebra of matrices over an arbitrary
field is an inner derivation, and every local inner derivation on the ring of
matrices over a finite ring generated by the identity element or the ring of
integers is an inner derivation. We also prove that every additive local inner
derivation on the Jordan algebra of symmetric matrices over an arbitrary field
is a derivation, and every local inner derivation on the Jordan ring of
symmetric matrices over a finite ring generated by the identity element or the
ring of integers is a derivation.
