17 citations · 44 across the 18 of their papers we have counts for
10 papers · 1 filter
On some mean matrix inequalities of dynamical interest
Igor Rivin
Let A be an n by n matrix with determinant 1. We show that for all n > 2 there exist dimensional strictly positive constants C_n such that the average over the orthogonal group of…
Differentiability of functions of matrices
Yury Grabovsky, Omar Hijab, Igor Rivin
Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves re…
Some observations on the simplex
Igor Rivin
We investigate the space of simplices in Euclidean Space
Simple estimates for ellipsoid measures
Igor Rivin
We write down estimates for the surface area, and more generally, integral mean curvatures of an ellipsoid E in n-dimensional Euclidean space in terms of the lengths of the major s…
Surface Area of Ellipsoids
Igor Rivin
We study the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of their major semi-axes. We write down an explicit formula as an integral…
A property of alternating groups
Henry Cejtin, Igor Rivin
We describe an efficient algorithm to write any element of the alternating group A_n as a product of two n-cycles (in particular, we show that any element of A_n can be so written…