Quaternion Hankel matrices have equal left and right ranks and correspond to linear recurrence relations with quaternion coefficients.
Aslaksen, Quaternionic determinants, in: Mathematical Conversations: Selections from The Mathematical Intelligencer, Springer, 2001, pp
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On the rank of quaternion Hankel matrices
Quaternion Hankel matrices have equal left and right ranks and correspond to linear recurrence relations with quaternion coefficients.