Localization theorems for matrices and bounds for the zeros of polynomials over a quaternion division algebra

2015/01/17 by Ahmad, Sk. Safique, Ali, Istkhar
#12E15 #15A18 #15A66 #34L15 #FOS: Mathematics #Numerical Analysis (math.NA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1502.08014

Abstract

In this paper, Ostrowski and Brauer type theorems are derived for the left and right eigenvalues of a quaternionic matrix. Generalizations of Gerschgorin type theorems are discussed for the left and the right eigenvalues of a quaternionic matrix. Thereafter a sufficient condition for the stability of a quaternionic matrix is given that generalizes the stability condition for a complex matrix. Finally, a characterization of bounds for the zeros of quaternionic polynomials is presented.

Related

• Location of the zeros of quaternionic polynomials using matrix tools
• Bounds for the Zeros of Quaternionic Polynomials and Regular Functions Using Matrix Techniques
• Stability of quaternion matrix polynomials
• On coneigenvalues of quaternion matrices: location and perturbation
• On the location of zeros of a quaternion polynomial