Opfer+Janovská: Linear equations and the Kronecker product in coquaternions


Gerhard Opfer, Drahoslava Janovská, Mitteilungen der Mathematischen Gesellschaft Hamburg, (33) 2013, 181-196, Hamburger Beiträge zur Angewandten Mathematik, Preprint 2013-05, May 2013, 13 p., dedicated to Lothar Reichel on the occasion of his 60th birthday.

Download: Linear equations and the Kronecker product in coquaternions

Abstract: We present the solution of the general linear system in n coquaternionic variables and m equations, and derive the Kronecker product from the matrix system AXB in coquaternions. It is shown, that the coquaternionic Kronecker product can be computed by means of dyadic coquaternionic products. The special matrix case Ax = b is also included. The one dimensional case, including Sylvester’s equation is solved and there are several, nontrivial, numerical examples.

Key words: Coquaternions, split quaternions, linear systems of equations in coquaternions, Ax = b in coquaternions, Kronecker product in coquaternions,
dyadic coquaternionic products, Sylvester’s equation in coquaternions.
AMS Subject classification: 11R52, 12E15, 12Y05, 15A06, 15A24.

Source: B. Schmeikal (unpublished, Jan. 2014), http://www.math.uni-hamburg.de/home/opfer/veroeffentlichungen/mathges2013.pdf

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