9 citations · 24 across the 5 of their papers we have counts for
9 papers
Tropical planar networks
Stephane Gaubert, Adi Niv
We show that every tropical totally positive matrix can be uniquely represented as the transfer matrix of a canonical totally connected weighted planar network. We deduce a uniquen…
Optimal Assignments with Supervisions
Adi Niv, Marie Maccaig, Sergei Sergeev
In this paper we provide a new graph theoretic proof of the tropical Jacobi identity, recently obtained in [AGN16]. We also develop an application of this theorem to optimal assign…
Tropical compound matrix identities
Marianne Akian, Stephane Gaubert, Adi Niv
We prove identities on compound matrices in extended tropical semirings. Such identities include analogues to properties of conjugate matrices, powers of matrices and~$\adj(A)\det(…
Tropical totally positive matrices
Stéphane Gaubert, Adi Niv
We investigate the tropical analogues of totally positive and totally nonnegative matrices. These arise when considering the images by the nonarchimedean valuation of the correspon…
Supertropical
Zur Izhakian, Adi Niv, Louis Rowen
Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version of the special linear group, whic…
Dependence of Supertropical Eigenspaces
Adi Niv, Louis Rowen
We study the pathology that causes tropical eigenspaces of distinct supertropical eigenvalues of a nonsingular matrix , to be dependent. We show that in lower dimensions the eig…
On pseudo-invereses of matrices and their characteristic polynomials in supertropical algebra
Adi Niv
The only invertible matrices in tropical algebra are diagonal matrices, permutation matrices and their products. However, the pseudo-inverse , defined as $\frac{adj(A)}{d…
Factorization of Tropical Matrices
Adi Niv
In contrast to the situation in classical linear algebra, not every tropically non-singular matrix can be factored into a product of tropical elementary matrices. We do prove the f…
Characteristic polynomials of supertropical matrices
Adi Niv
Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we investigate eigenvalues, characteristic polynomials and coefficients of characteri…