A remark on reversible matrices
M. S. Macphail · Proceedings of the American Mathematical Society · 1954
It is further stated in [1, p. 50] that the Ck are bounded. This is questioned in [4], where it is pointed out that if the Ck were generally bounded they would have to be almost all zero, but this remark does not dispose of the matter, for it might conceivably be a true theorem that for each reversible matrix the Ck are almost all zero. (For rowfinite matrices, all Ck vanish; [3].) The example given in [4, p. 47] seems inconclusive. The purpose of this note is to show by a very simple example that in fact the ck need not be bounded. Consider the transformation