English

Geometric Matrix Midranges

Optimization and Control 2020-05-29 v2

Abstract

We define geometric matrix midranges for positive definite Hermitian matrices and study the midrange problem from a number of perspectives. Special attention is given to the midrange of two positive definite matrices before considering the extension of the problem to N>2N > 2 matrices. We compare matrix midrange statistics with the scalar and vector midrange problem and note the special significance of the matrix problem from a computational standpoint. We also study various aspects of geometric matrix midrange statistics from the viewpoint of linear algebra, differential geometry and convex optimization.

Keywords

Cite

@article{arxiv.1907.04188,
  title  = {Geometric Matrix Midranges},
  author = {Cyrus Mostajeran and Christian Grussler and Rodolphe Sepulchre},
  journal= {arXiv preprint arXiv:1907.04188},
  year   = {2020}
}