  In [1] it is shown that recurrent neural networks (RNNs) can learn - in a
metric entropy optimal manner - discrete time, linear time-invariant (LTI)
systems. This is effected by comparing the number of bits needed to encode the
approximating RNN to the metric entropy of the class of LTI systems under
consideration [2, 3]. The purpose of this note is to provide an elementary
self-contained proof of the metric entropy results in [2, 3], in the process of
which minor mathematical issues appearing in [2, 3] are cleaned up. These
corrections also lead to the correction of a constant in a result in [1] (see
Remark 2.5).
