2012/12/06 by Olga Y. Kushel, Kushel, Olga Y.
Computer Science · Mathematics · #FOS: Mathematics #Graph theory and applications #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Primary 15A48 Secondary 15A18 15A75 #Rings and Algebras (math.RA) #Spectral Theory (math.SP) #math.RA #math.SP #msc:15A18 #msc:15A48 #msc:15A75
paper · pdf · doi:10.48550/arxiv.1212.1387
23 pages
arxiv created 2012/12/06 · openalex publication_date 2012/12/06 · arxiv updated 2012/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish the eigenvalue interlacing property (i.e. the smallest real eigenvalue of a matrix is less than the smallest real eigenvalue of any its principal submatrix) for the class of matrices, introduced by Kotelyansky (all principal and all almost principal minors of these matrices are positive). We show that certain generalizations of Kotelyansky and totally positive matrices also possess this property. We prove some interlacing inequalities for the other eigenvalues of Kotelyansky matrices.