Generalisation of the Perron-Frobenius theory to matrix pencils

DOI10.1016/j.laa.2007.07.004zbMath1130.15007OpenAlexW2071119554MaRDI QIDQ2463608

Reinhard Nabben, Elena Virnik, Volker Mehrmann

Publication date: 14 December 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2007.07.004

zbMATH Keywords

differential-algebraic equationdescriptor systemtractability indexmatrix pencilsPerron-Frobenius theoremdifferentiation indexprojector chain

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Matrix pencils (15A22)

Related Items (6)

The level set method for the two-sided max-plus eigenproblem ⋮ Stability radius of implicit dynamic equations with constant coefficients on time scales ⋮ The existence and uniqueness of eigenvalues for monotone homogeneous mapping pairs ⋮ Stability analysis of positive descriptor systems ⋮ On the problem Ax=\lambda Bx in max algebra: every system of intervals is a spectrum ⋮ Stability Analysis of Implicit Difference Equations Under Restricted Perturbations

Cites Work

• A primer of Perron--Frobenius theory for matrix polynomials
• Index determination and calculation of consistent initial values for DAEs
• Relations between Perron-Frobenius results for matrix pencils
• Canonical projectors for linear differential algebraic equations
• Perron-Frobenius properties of \(Ax-\lambda Bx\)
• Z-Pencils
• Perron-frobenius theory for a generalized eigenproblem
• Positive 1D and 2D systems
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