2026-06-27T22:59:39Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/730712024-06-05T16:21:05Zcom_20.500.14352_14col_20.500.14352_15

Normal Tropical (0,−1)-Matrices and Their Orthogonal Sets Bakhadly, B. Guterman, A. Puente Muñoz, María Jesús De La 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. 2023-06-22T12:42:16Z 2023-06-22T12:42:16Z 2023-06-22T12:42:16Z 2023-02 journal article https://hdl.handle.net/20.500.14352/73071 1072-3374 10.1007/s10958-023-06305-4 eng MTM2016-76808-P PID-2019-10770 GB-I00 open access Springer