Groups of singular alternating sign matrices
Citation
O'Brien, C. and Quinlan, R. (2025) 'Groups of singular alternating sign matrices', Electronic Journal of Linear Algebra, 41, 288-303, available: https://doi.org/10.13001/ela.2025.8715.
Date
2025-05-20Author
O'Brien, Cian
Quinlan, Rachel
Peer Reviewed
YesMetadata
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O'Brien, C. and Quinlan, R. (2025) 'Groups of singular alternating sign matrices', Electronic Journal of Linear Algebra, 41, 288-303, available: https://doi.org/10.13001/ela.2025.8715.
Abstract
We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs) and present
several constructions of such groups. It is shown that every finite group is isomorphic to a group of singular ASMs, with a
singular idempotent ASM as its identity element. The relationship between the size, the rank, and the possible multiplicative
orders of singular ASMs is explored.
Keywords
Alternating sign matrixASM
Matrix group