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Ordering of nonnegative definite matrices with applications to comparison of linear models. Linear Algebra Appl. 70, 67–71 (1985) 38. : Robust local max-min filters by normalized power-weighted filtering. In: Proceedings of IEEE 17th International Conference of the Pattern Recognition (ICPR’04), vol 1, pp. 696–699, (2004) 39. : Supervised ordering in R n : Application to morphological processing of hyperspectral images. IEEE Trans. Image Process. 20(11), 3301–3308 (2011) 40. : Mathematical morphology for vector images using statistical depth.

Consequently, we can use the asymptotic values of the CHMM with P → +∞ and P → −∞ to define approximations to the supremum and infimum of a set of matrices. 20) chmm = inf (A) = lim κ P (A) . 4 depicts an example of the supremum/infimum obtained for a set A of 3 PDS(2) matrices using the CHMM paradigm. More precisely, the values of κ P (A) for six different orders are given (P = 5,P = 10,P = 20,P = −5,P = −10,P = −20); which can be compared again with the results obtained using Minkowski and Achmm can be interpreted geometmatrix mean.

On the averaging of symmetric positive-definite tensors. J. Elast. 82, 273–296 (2006) 26. : Geometric means of positive operators. Kyungpook Math. J. 49, 167–181 (2009) 27. : A multivariable extension of two-variable matrix means. SIAM J. Matrix Anal. Appl. 32, 385–393 (2011) 2 The Riemannian Mean of Positive Matrices 51 28. : Functional calculus for sesquilinear forms and the purification map. Rep. Math. Phys. 8, 159–170 (1975) 29. : Probability measures on metric spaces of nonpositive curvature.

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