An open question was raised by Qi et al. (J Comput Appl Math 221:150–1571, 2008) in studying diffusion kurtosis imaging which involves a diffusion kurtosis tensor \({\mathcal {W}}\) and a diffusion tensor D. This open question focuses on the calculation of the D-eigenvalues of \({\mathcal {W}}\) and can be expressed as: How to compute the D-eigenvalues if D is not positive definite? In this paper, we partially answer this question: when D is positive semi-definite, by using the Moore–Penrose inverse of D, we propose a Z-eigenpair method to compute all D-eigenpairs of \({\mathcal {W}}\) . In addition, when D is positive definite, we also propose a Z-eigenpair method to compute all D-eigenpairs of \({\mathcal {W}}\) . Numerical examples show the correctness and effectiveness of our methods.
