Algebraic proof of the equivalence of two variants of the cut-norm for multidimensional symmetric matrices
Abstract
The paper proves the equivalence of two special matrix norms. Both norms arise in models formulated in terms of interactions between binary variables. One norm is associated with the interaction of these variables within a single group, while the other is related to the interaction of variables from different groups. The statement allows for an easy transfer of meaningful results from the second (simpler) case to the first.
About the Authors
P. N. Shvedkov
Belarusian State University
Belarus
Belarus
Minsk
K. V. Lykov
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
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Review
For citations:
Shvedkov P.N., Lykov K.V. Algebraic proof of the equivalence of two variants of the cut-norm for multidimensional symmetric matrices. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(1):34-43. (In Russ.)
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