  We examine when a matrix whose elements are differentiable functions in one
variable commutes with its derivative. This problem was discussed in a letter
from Issai Schur to Helmut Wielandt written in 1934, which we found in
Wielandt's Nachlass. We present this letter and its translation into English.
The topic was rediscovered later and partial results were proved. However,
there are many subtle observations in Schur's letter which were not obtained in
later years. Using an algebraic setting, we put these into perspective and
extend them in several directions. We present in detail the relationship
between several conditions mentioned in Schur's letter and we focus in
particular on the characterization of matrices called Type 1 by Schur. We also
present several examples that demonstrate Schur's observations.
