Permutable Symmetric Hadamard Matrices in Quaternion Algebra and Engineering Applications
2021 ◽
Vol 61
◽
pp. 17-40
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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.
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2019 ◽
Vol 13
(3)
◽
pp. 5653-5664
2017 ◽
Vol 4
(1)
◽
pp. 23-30
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