Eigenvalue problem for some special class of anti-triangular matrices

2014/03/14 by Hiroyuki Ochiai, Makiko Sasada, Ochiai, Hiroyuki +5
Mathematics · #15B51 #FOS: Mathematics #Primary 15A18 #Probability (math.PR) #Rings and Algebras (math.RA) #Secondary 60K35 #math.PR #math.RA #msc:15A18 #msc:15B51 #msc:60K35

paper · pdf · doi:10.48550/arxiv.1403.6797

arxiv created 2014/03/14 · arxiv updated 2014/03/27

Abstract

We study the eigenvalue problem for some special class of anti-triangular matrices. Though the eigenvalue problem is quite classical, as far as we know, almost nothing is known about properties of eigenvalues for anti-triangular matrices. In this paper, we show that there is a nice class of anti-triangular matrices whose eigenvalues are given explicitly by their elements. Moreover, this class contains several interesting subclasses which we characterize in terms of probability measures. We also discuss the application of our main theorem to the study of interacting particle systems, which are stochastic processes studied in extensive literature.

Related

• Generalization of some results concerning eigenvalues of a certain class of matrices and some applications
• Eigenvectors of random matrices: A survey
• Recent advances on eigenvalues of matrix-valued stochastic processes
• An algorithm for constructing doubly stochastic matrices for the inverse eigenvalue problem
• Limiting eigenvectors of outliers for Spiked Information-Plus-Noise type matrices