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Information × Registration Number 0223U005084, 0123U103533 , R & D reports Title Application of quaternions in Laplacian constrained Gaussian graphical models and graphical neural networks popup.stage_title Head Kyrchei Ivan I., Доктор фізико-математичних наук Registration Date 14-12-2023 Organization Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine popup.description2 Some properties of the matrix representations of the complex unitary graph with amplification to the quaternion unitary graph with amplification are extended. Matrix representations of the unit quaternion graph with gain, such as conjugate, Laplacian, and via incidence matrices, are investigated. A combinatorial description of the determinant of the Laplacian matrix is given. To solve the problem of determining the determinant of a square matrix with non-commutative elements, the theory of row-column determinants, developed by one of the authors, was used. It is expected that many other results from the theories of signed and complex unitary graphs with gain can be generalized in this way to the quaternion case. Product Description popup.authors Pelykh Volodymyr O. Taistra Yurii V. popup.nrat_date 2023-12-14 Close