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Permutable Symmetric Hadamard Matrices in Quaternion Algebra and Engineering Applications

Mikhail V. Kharinov, Marin Drinov Academic Publishing House

Abstract: In this paper, aiming to develop the group and out-of-group formalization of the symmetry concept, the preservation of a matrix symmetry after row permutation is considered by the example of the maximally permutable \emph{normalized} Hadamard matrices which row and column elements are either plus or minus one. These matrices are used to extend the additive decomposition of a linear operator into symmetric and skew-symmetric parts using several commuting operations of the Hermitian conjugation type, for the quaternionic generalization of a vector cross product, as well as for creating educational puzzles and other applications.
Keywords: symmetric / Quaternion / Hadamard / symmetry / row / permutable / skew / Algebra / matrix / minus

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