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Algebraic techniques for least squares problems in commutative quaternionic theory

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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 AX≈B and… Click to show full abstract

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 AX≈B and AXC≈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.

Keywords: squares problems; commutative quaternion; least squares; commutative quaternionic; problems commutative; algebraic techniques

Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2020

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