2020/03/29 by Himadri Lal Das, M. Rajesh Kannan, Das, Himadri Lal +1
Computer Science · Engineering · Mathematics · #15A15 #15A18 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2003.13095
openalex publication_date 2020/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that the set of all n \× n matrices with distinct\neigenvalues is a dense subset of the set of all real or complex n \× n \nmatrices. In [Hartfiel, D. J. Dense sets of diagonalizable matrices. Proc.\nAmer. Math. Soc., 123(6): 1669-1672, 1995.], the author established a necessary\nand sufficient condition for a subspace of the set of all n \× n matrices\nto have a dense subset of matrices with distinct eigenvalues. We are interested\nin finding a few necessary and sufficient conditions for a subset of the set of\nall n \× n real or complex matrices to have a dense subset of matrices\nwith distinct eigenvalues. Some of our results are generalizing the results of\nHartfiel. Also, we study the existence of dense subsets of matrices with\ndistinct singular values, distinct analytic eigenvalues, and distinct analytic\nsingular values, respectively, in the subsets of the set of all real or complex\nmatrices.\n