Publications (26)
Orthogonality for tropical normal matrices
Bakhad Bakhadly, Alexander Guterman, MarÃa Jesús de la Puente
We study pairs of mutually orthogonal normal matrices with respect to tropical multiplication. Minimal orthogonal pairs are characterized. The diameter and girth of three graphs ar…
Integrability of matrices
Suren Danielyan, Alexander Guterman, Elena Kreines +1
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or no…
Linear varieties and matroids with applications to the Cullis' determinant
Alexander Guterman, Andrey Yurkov
Let be a vector space of rectangular matrices annihilating the Cullis' determinant. We show that , extending Dieudonn{é}'s result on the dimens…
Linear independence over tropical semirings and beyond
Marianne Akian, Stephane Gaubert, Alexander Guterman
We investigate different notions of linear independence and of matrix rank that are relevant for max-plus or tropical semirings. The factor rank and tropical rank have already rece…
Additive preservers of permanent rank
Alexander Guterman, Bojan Kuzma, Leonid Ovchinnikov
The permanent rank of a matrix is the size of the maximal square submatrix in which has a nonzero permanent. In this paper we characterize additive transformations whi…
Algebras of slowly growing length
Alexander Guterman, Dmitry Kudryavtsev
We investigate the class of finite dimensional not necessary associative algebras that have slowly growing length, that is, for any algebra in this class its length is less than or…