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A note on resolving the inconsistency of one-sided max-plus linear equations

Pingke Li (2019)

Kybernetika

When a system of one-sided max-plus linear equations is inconsistent, its right-hand side vector may be slightly modified to reach a consistent one. It is handled in this note by minimizing the sum of absolute deviations in the right-hand side vector. It turns out that this problem may be reformulated as a mixed integer linear programming problem. Although solving such a problem requires much computational effort, it may propose a solution that just modifies few elements of the right-hand side vector,...

A note on the determinant of a Toeplitz-Hessenberg matrix

Mircea Merca (2013)

Special Matrices

The nth-order determinant of a Toeplitz-Hessenberg matrix is expressed as a sum over the integer partitions of n. Many combinatorial identities involving integer partitions and multinomial coefficients can be generated using this formula.

A note on the matrix Haffian.

Heinz Neudecker (2000)

Qüestiió

This note contains a transparent presentation of the matrix Haffian. A basic theorem links this matrix and the differential ofthe matrix function under investigation, viz ∇F(X) and dF(X).Frequent use is being made of matrix derivatives as developed by Magnus and Neudecker.

A Note on the Permanental Roots of Bipartite Graphs

Heping Zhang, Shunyi Liu, Wei Li (2014)

Discussiones Mathematicae Graph Theory

It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing...

A note on the scalar Haffian.

Heinz Neudecker (2000)

Qüestiió

In this note a uniform transparent presentation of the scalar Haffian will be given. Some well-known results will be generalized. A link will be established between the scalar Haffian and the derivative matrix as developed by Magnus and Neudecker.

A note on ultrametric matrices

Xiao-Dong Zhang (2004)

Czechoslovak Mathematical Journal

It is proved in this paper that special generalized ultrametric and special 𝒰 matrices are, in a sense, extremal matrices in the boundary of the set of generalized ultrametric and 𝒰 matrices, respectively. Moreover, we present a new class of inverse M -matrices which generalizes the class of 𝒰 matrices.

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