Means for fixed rank PSD matrices (Q782525)

The geometric mean for positive semidefinite matrices for projections of fixed rank were introduced by \textit{S. Bonnabel} and \textit{R. Sepulchre} [SIAM J. Matrix Anal. Appl. 31, No. 3, 1055--1070 (2010; Zbl 1220.47025)] and \textit{E. Batzies} et al. [Linear Algebra Appl. 466, 83--101 (2015; Zbl 1315.53037)], based on the theory of Grassmann manifolds. In the case of full rank matrices, this mean coincides with the one corresponding to the theory of \textit{F. Kubo} and \textit{T. Ando} [Math. Ann. 246, 205--224 (1980; Zbl 0412.47013)]. In this work, the author extends it to a general theory of means of positive semidefinite matrices of fixed rank.