Abstract: Several spectral radii formulas for infinite bounded non-negative matrices in max algebra are obtained. We also prove some Perron–Frobenius type results for such matrices. In particular, we obtain results on block triangular forms, which are similar to results on Frobenius normal form of $n \times n$ matrices. Some continuity results are also established.Keywords: non-negative matrices, infinite bounded matrices, max algebra, Bonsall’s cone spectral radius, eigenvalues, continuityPublished in DiRROS: 30.05.2024; Views: 116; Downloads: 113 Full text (1,77 MB)This document has many files! More...
Abstract: We present a procedure which enables the computation and the description of structures of isotropy subgroups of the group of complex orthogonal matrices with respect to the action of $^\ast$congruence on Hermitian matrices. A key ingredient in our proof is an algorithm giving solutions of a certain rectangular block (complex-alternating) upper triangular Toeplitz matrix equation.Keywords: isotropy groups, matrix equations, complex orthogonal matrices, Hermitian matrices, Toeplitz matricesPublished in DiRROS: 06.05.2024; Views: 237; Downloads: 141 Full text (651,15 KB)This document has many files! More...
Abstract: We find an algorithmic procedure that enables the computation and description of the structure of the isotropy subgroups of the group of complex orthogonal matrices with respect to the action of similarity on complex symmetric matrices. A key step in our proof is to solve a certain rectangular block upper triangular Toeplitz matrix equation.Keywords: isotropy groups, matrix equations, orthogonal matrices, symmetric matrices, Toeplitz matricesPublished in DiRROS: 08.04.2024; Views: 237; Downloads: 86 Full text (2,08 MB)This document has many files! More...
