Ievgen Bilokopytov

(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.

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