(Department of Mathematics, University of Manitoba)
From Principal Minor Assignment Problem To Characterization Of The Isometries On Hilbert Spaces, Through Volumes Of Parallelepipeds
|Date||Friday, May 10, 2019|
We show that two parallelepipeds in the Euclidean space with equal volumes of the corresponding faces are isometric. The proof of this geometric result is reduced to a well-known combinatorial matrix problem. We extend the solution of the latter problem to the case of infinite matrices, which allows us to state a version of the original result in the infinite-dimensional context. As an application we obtain a new characterization of isometries of Hilbert spaces.