Regularization and Interpolation of Positive Matrices

We construct certain matricial analogues of mass transport for positive-definite matrices of equal trace. The framework aims to devise ways of interpolating positive-definite matrices that tradeoff between “aligning up their eigenstructure” and “scaling the corresponding eigenvalues.” Motivation for the work is provided by power spectral analysis of multivariate time series where linear interpolation between matrix-valued power spectra generates push-pop unrealistic and undesirable artifacts.