How to deal with complex eigenvalues when computing fractional anisotropy. I am attempting to measure the laminar flow, or rather how non-laminar a velocity field is. In order to do this I am looking at Fractional Anisotropy. The FA is calculated from the eigen values of the diffusion tensor, which is being treated as a 3x3 matrix, using the following formulation (identical to the wikipedia link) $\mbox{FA} = \sqrt{\frac{3}{2}}\frac{\sqrt{(\lambda_1 - \hat{\lambda} )^2 + (\lambda_2 - \hat{\lambda} )^2 + (\lambda_3 - \hat{\lambda} )^2}}{\sqrt{\lambda_1^2 + \lambda_2^2 + \lambda_3^2}}$ where $\hat{\lambda} = \frac{\lambda_1 + \lambda_2 + \lambda_3}{3}$ My question is if the 3 eigenvalues of the diffusion tensor are not all real then how do I deal with the complex eigenvalues? first guess is to do the dumb thing and just ignore the imaginary part of the eigenvalues.

Whether it is worth examining is not a mathematical question, I think. But isn't the diffusion tensor a symmetric matrix? If so, its eigenvalues are real.