  Recently, the quaternionic quantum walk was formulated by the first author as
a generalization of discrete-time quantum walks. We treat the right eigenvalue
problem of quaternionic matrices to analysis the spectra of its transition
matrix. The way to obtain all the right eigenvalues of a quaternionic matrix is
given. From the unitary condition on the transition matrix of the quaternionic
quantum walk, we deduce some properties about it. Our main results, Theorem
5.3, determine all the right eigenvalues of a quaternionic quantum walk by use
of those of the corresponding weighted matrix. In addition, we give some
examples of quaternionic quantum walks and their right eigenvalues.
