A Note on a Generalization of Boolean Matrix Theory

Yoeli, Michael

doi:10.1080/00029890.1961.11989717

Cited by 40 publications

(34 citation statements)

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“…(see Theorem 3.6 and Proposition 3.7). These results are extended to the supertropical setting from the results obtained over the tropical structure in [31] and [28], regarding these closure operations.…”

Section: Introductionmentioning

confidence: 81%

On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra

Niv

2015

Linear Algebra and its Applications

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International audienceThe only invertible matrices in tropical algebra are diagonal matrices, permutation matrices and their products. However, the pseudo-inverse A ∇ , defined as 1 det(A) adj(A), with det(A) being the tropical permanent (also called the tropical determinant) of a matrix A, inherits some classical algebraic properties and has some surprising new ones. Defining B and B to be tropically similar if B = A ∇ BA, we examine the characteristic (max-)polynomials of tropically similar matrices as well as those of pseudo-inverses. Other miscellaneous results include a new proof of the identity for det(AB) and a connection to stabilization of the powers of definite matrices

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Section: Introductionmentioning

confidence: 81%

On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra

Niv

2015

Linear Algebra and its Applications

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“…, n}. This definition coincides with the definition of a tropical permanent, due to the fact that there is no negation in tropical arithmetic [21,15]. The permanent of a matrix A is often denoted by per(A) or perm(A) in the literature, see, e.g., [17].…”

Section: Tropical Linear Algebramentioning

confidence: 93%

“…An (n+1)×(n+1) matrix A is called regular if A contains at least one element different from 0 • in each row. As in [21] we define the tropical determinant…”

Section: Tropical Linear Algebramentioning

confidence: 99%

Second main theorem in the tropical projective space

Korhonen

Tohge

2016

Advances in Mathematics

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Abstract. Tropical Nevanlinna theory, introduced by Halburd and Southall as a tool to analyze integrability of ultra-discrete equations, studies the growth and complexity of continuous piecewise linear real functions. The purpose of this paper is to extend tropical Nevanlinna theory to n-dimensional tropical projective spaces by introducing a natural characteristic function for tropical holomorphic curves, and by proving a tropical analogue of Cartan's second main theorem. It is also shown that in the 1-dimensional case this result implies a known tropical second main theorem due to Laine and Tohge.

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“…L'utilité et la rapidité d'exécution de l'algorithme de Warshall nous a incité à étudier sa généralisation aux matrices définies sur une structure algé-brique que nous appelons « g-senü-anneau » (d'après M. Yoeli [6]) et dont l'algèbre booléenne B(0, 1) est un cas particulier.…”

Section: Introductionunclassified

Généralisation de l'algorithme de Warshall

Robert¹,

Ferland²

1968

R.I.R.O.

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A Note on a Generalization of Boolean Matrix Theory

Cited by 40 publications

References 1 publication

On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra

On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra

Second main theorem in the tropical projective space

Généralisation de l'algorithme de Warshall

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