INVESTIGADORES
GHIGLIONI Eduardo Mario
artículos
Título:
Hyperbolicity of the Karcher Mean
Autor/es:
GHIGLIONI, EDUARDO; LIM, YONGDO
Revista:
LINEAR ALGEBRA AND ITS APPLICATIONS
Editorial:
ELSEVIER SCIENCE INC
Referencias:
Año: 2022
ISSN:
0024-3795
Resumen:
The main concern of this paper is the Karcher mean of linearly independent triples (A,B,C) on the hyperbolic manifold of positive definite matrices of determinant 1. We show that the Karcher mean is of the form Lambda(A,B,C)=xA + y(B+C) 0 < x,y and x +2y < 1under the trace condition Tr(AB^{-1})= Tr(BC^{-1}). We further find an invertible hyperbolic matrix M depending only on the trace values and such that [ x y] = M[cosh(theta) senh(theta)] for some unique theta.
