On the pure imaginary quaternionic solutions of the Hurwitz matrix equations

In this paper, we consider the number of n × n pure imaginary quaternionic solutions to the Hurwitz matrix equations given byTiTj*+TjTi*=2δijI.For n = 2m, the maximum number of solutions is determined if m ≢ 0 (mod 4). The case m ≡ 0 (mod 4) is also discussed.