RT Journal Article
T1 Normal Tropical (0,−1)-Matrices and Their Orthogonal Sets
A1 Bakhadly, B.
A1 Guterman, A.
A1 Puente Muñoz, María Jesús De La
AB Square matrices A and B are orthogonal if AʘB = Z = BʘA, where Z is the matrix entries equal to 0, and ʘ is the tropical matrix multiplication. We study orthogonality for normal matrices over the set {0, −1}, endowed with tropical addition and multiplication. To do this, we investigate the orthogonal set of a matrix A, i.e., the set of all matrices orthogonal to A. In particular, we study the family of minimal elements inside the orthogonal set, called a basis. Orthogonal sets and bases are computed for various matrices and matrix sets. Matrices whose bases are singletons are characterized. Orthogonality and minimal orthogonality are described in the language of graphs. The geometric interpretation of the results obtained is discussed.
PB Springer
SN 1072-3374
YR 2023
FD 2023-02
LK https://hdl.handle.net/20.500.14352/73071
UL https://hdl.handle.net/20.500.14352/73071
LA eng
NO Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 24, No. 1, pp. 5–30, 2022.
NO Ministerio de Economía y Competitividad (MINECO)
NO Ministerio de Ciencia e Innovación (MICINN)
DS Docta Complutense
RD 7 abr 2025