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: 24; Downloads: 2 Full text (651,15 KB)This document has many files! More...
Abstract: We extend our previous result on the behaviour of the quadratic part of a complex points of a small ${\mathcal C}^2$-perturbation of a real $4$-manifold embedded in a complex $3$-manifold. We describe the change of the structure of the quadratic normal form of a complex point. It is an immediate consequence of a theorem clarifying how small perturbations can change the bundle of a pair of one arbitrary and one symmetric $2 \times 2$ matrix with respect to an action of a certain linear group.Keywords: CR manifolds, closure graphs, complex points, normal forms, perturbationsPublished in DiRROS: 06.05.2024; Views: 23; Downloads: 3 Full text (929,58 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: 77; Downloads: 42 Full text (2,08 MB)This document has many files! More...
