A further look into combinatorial orthogonality
Simone Severini, Ferenc Sz\"oll\H{o}si
TL;DR
This paper classifies strongly quadrangular matrices up to degree 5, identifying the smallest matrices that do not support unitaries and analyzing submatrices that prevent such support.
Contribution
It provides a complete classification of strongly quadrangular matrices up to degree 5 and identifies key submatrices obstructing unitary support.
Findings
Smallest strongly quadrangular matrices not supporting unitaries have degree 5
Complete classification of strongly quadrangular matrices up to degree 5
Identification of submatrices preventing (0,1)-matrices from supporting unitaries
Abstract
Strongly quadrangular matrices have been introduced in the study of the combinatorial properties of unitary matrices. It is known that if a (0, 1)-matrix supports a unitary then it is strongly quadrangular. However, the converse is not necessarily true. In this paper, we fully classify strongly quadrangular matrices up to degree 5. We prove that the smallest strongly quadrangular matrices which do not support unitaries have exactly degree 5. Further, we isolate two submatrices not allowing a (0, 1)-matrix to support unitaries.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsgraph theory and CDMA systems · Matrix Theory and Algorithms · Advanced Optimization Algorithms Research