  We consider certain matricial analogues of optimal mass transport of positive
definite matrices of equal trace. The framework is motivated by the need to
devise a suitable geometry for interpolating positive definite matrices in ways
that allow controlling the apparent tradeoff between "aligning up their
eigenstructure" and "scaling the corresponding eigenvalues". Indeed, motivation
for this work is provided by power spectral analysis of multivariate time
series where, linear interpolation between matrix-valued power spectra
generates push-pop artifacts. Push-pop of power distribuion is objectionable as
it corresponds to unrealistic response of scatterers.
