A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...

in this paper we study the impact of minkowski metric matrix on a projection in theminkowski space m along with their basic algebraic and geometric properties.the relationbetween the m-projections and the minkowski inverse of a matrix a in the minkowski spacemis derived. in the remaining portion commutativity of minkowski inverse in minkowski spacem is analyzed in terms of m-projections as an a...

An attractive candidate for the geometric mean of m positive definite matrices A1, . . . , Am is their Riemannian barycentre G. One of its important properties, monotonicity in the m arguments, has been established recently by J. Lawson and Y. Lim. We give a much simpler proof of this result, and prove some other inequalities. One of these says that, for every unitarily invariant norm, |||G||| ...

In this paper, we analyze the process of “assembling” new matrix geometric means from existing ones, and show what new means can be found, and what cannot be done because of group-theoretical obstructions. We show that for n = 4 a new matrix mean exists which is simpler to compute than the existing ones. Moreover, we show that for n > 4 the existing strategies of composing matrix means and taki...