Majorization in Euclidean Geometry and Beyond

0433898 - ÚI 2015 RIV US eng J - Článek v odborném periodiku
Fiedler, Miroslav
Majorization in Euclidean Geometry and Beyond.
Linear Algebra and Its Applications. Roč. 466, 1 February (2015), s. 233-240. ISSN 0024-3795. E-ISSN 1873-1856
Institucionální podpora: RVO:67985807
Klíčová slova: Majorization * Doubly stochastic matrix * Euclidean simplex * Star * Regular simplex * Volume of a simplex
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.965, rok: 2015

We relate the well known notion of majorization to the behavior of a pair of simplices in a Euclidean n-space. We obtain a geometrical meaning for the determinant of the involved doubly stochastic matrix. Independently, a basic theorem about volumes of simplices contained one in another, even if of different dimensions, is proved. Some related geometric questions are also presented.
Trvalý link: http://hdl.handle.net/11104/0238061