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Seminar: An application of the non-orthogonality graph
- Date
- January 21, 2026
- Time
- 11:10 a.m. - 12:00 p.m. ET
- Location
- ENG-210 and virtually via zoom
- Open To
- All faculty, staff, students and guests are welcome to attend
- Contact
- Pawel Pralat (pralat@torontomu.ca)
Speaker: Eugene Bilokopytov, University of Alberta
Title: An application of the non-orthogonality graph
Abstract: Let $X$ be a set in a Hilbert space $H$. Join $x$ and $y$ in $X$ by an edge if they are not orthogonal. Working with the obtained graph we will prove that if $X$ is connected, then a map from $X$ into $H$ extends to a self-isometry of $H$ if and only if that map preserves volumes of parallelepipeds spanned by finite subsets of $X$. Another application of this method is the result that two parallelepipeds are equal (as geometric figures) if and only if the corresponding faces of all dimensions have the same volumes.