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Displaying 381 – 400 of 3007

An extension of a result of Lewis.

Tam, Tin-Yau (1999)

ELA. The Electronic Journal of Linear Algebra [electronic only]

An extension of the perturbation analysis for the Drazin inverse.

Castro-Gonzalez, N., Martinez-Serrano, M.F., Robles, J. (2011)

ELA. The Electronic Journal of Linear Algebra [electronic only]

An idempotent algorithm for a class of network-disruption games

William M. McEneaney, Amit Pandey (2016)

Kybernetika

A game is considered where the communication network of the first player is explicitly modelled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modelled through expectations over idempotent probability measures. The idempotent probabilities are conditioned by observational data, the arrival of which may have been delayed along the communication network. This induces a game where the state space consists of the network delays. Even...

An identity between the determinant and the permanent of Hessenberg-type matrices

Carlos Martins da Fonseca (2011)

Czechoslovak Mathematical Journal

In this short note we provide an extension of the notion of Hessenberg matrix and observe an identity between the determinant and the permanent of such matrices. The celebrated identity due to Gibson involving Hessenberg matrices is consequently generalized.

An implementation of the fast Givens transformations on a MIMD computer

J. S. Kowalik, S. P. Kumar, E. R. Kamgnia (1983)

Applicationes Mathematicae

An improved characterisation of the interior of the completely positive cone.

Dickinson, Peter J.C. (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

An improvement of an inequality of Fiedler leading to a new conjecture on nonnegative matrices

Assaf Goldberger, Neumann, Michael (2004)

Czechoslovak Mathematical Journal

Suppose that $A$ is an $n \times n$ nonnegative matrix whose eigenvalues are $λ = ρ (A), λ_{2}, ..., λ_{n}$ . Fiedler and others have shown that $det (λ I - A) \leq λ^{n} - ρ^{n}$ , for all $λ > ρ$ , with equality for any such $λ$ if and only if $A$ is the simple cycle matrix. Let $a_{i}$ be the signed sum of the determinants of the principal submatrices of $A$ of order $i \times i$ , $i = 1, ..., n - 1$ . We use similar techniques to Fiedler to show that Fiedler’s inequality can be strengthened to: $det (λ I - A) + \sum_{i = 1}^{n - 1} ρ^{n - 2 i} | a_{i} | {(λ - ρ)}^{i} \leq λ^{n} - ρ^{n}$ , for all $λ \geq ρ$ . We use this inequality to derive the inequality that: $\prod_{2}^{n} (ρ - λ_{i}) \leq ρ^{n - 2} \sum_{i = 2}^{n} (ρ - λ_{i})$ . In the spirit of a celebrated conjecture due to Boyle-Handelman,...