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    A generalized quaternionic sequence with Vietoris' number components
    (Univ Nis, Fac Sci Math, 2023) Senturk, Gulsum Yeliz
    In this investigation, the aim is to determine a generalized quaternionic sequence with Vietoris' number components depending on 2-parameters & alpha; and 13. Considering specific real values & alpha; and 13, various types of classical quaternionic sequence with Vietoris' number components can be obtained as real, split, split-semi and so on. The fundamental algebraic structures, several classical expressions, a two and three term recurrence relations are identified, as well as Catalan-like, generating function and Binet-like formulas. Furthermore, a determinantal approach is used to generate the generalized quaternionic sequence with Vietoris' number components.
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    MATRIX THEORY OVER DGC NUMBERS
    (Editura Bibliotheca-Bibliotheca Publ House, 2023) Gurses, Nurten; Senturk, Gulsum Yeliz
    Classical matrix theory for real, complex and hypercomplex numbers is a well-known concept. Is it possible to construct matrix theory over dual-generalized complex (DGC) matrices? The answer to this question is given in this paper. The paper is constructed as follows. Firstly, the fundamental concepts for DGC matrices are introduced and DGC special matrices are defined. Then, theoretical results related to eigenvalues/eigenvectors are obtained and universal similarity factorization equality (USFE) regarding to the dual fundamental matrix are presented. Also, spectral theorems for Hermitian and unitary matrices are introduced. Finally, due to the importance of unitary matrices, a method for finding a DGC unitary matrix is stated and examples for spectral theorem are given.
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    Similarity relations and exponential of dual-generalized complex matrices
    (Ovidius Univ Press, 2023) Gurses, Nurten; Senturk, Gulsum Yeliz
    In this study, taking into account the fundamental properties of dual-generalized complex (DGC) matrices, various types of similarity relations are introduced considering coneigenvalues/coneigenvectors via di erent conjugates. The exponential version of DGC matrices are identified and then their theoretical characteristic theorems are obtained. Finally, examples for DGC matrix exponential are given.