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Algebraic techniques for least squares problems in commutative quaternionic theory
Author(s) -
Zhang Dong,
Guo Zhenwei,
Wang Gang,
Jiang Tongsong
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6135
Subject(s) - quaternion , mathematics , commutative property , algebraic number , algebra over a field , representation (politics) , pure mathematics , mathematical analysis , geometry , law , politics , political science
Due to the rise of commutative quaternion in Hopfield neural networks, digital signal, and image processing, one encounters the approximate solution problems of the commutative quaternion linear equations A X ≈ B and A X C ≈ B . This paper, by means of real representation and complex representation of commutative quaternion matrices, introduces concepts of norms of commutative quaternion matrices and derives two algebraic techniques for finding solutions of least squares problems in commutative quaternionic theory.