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Cramer’s rule for quaternionic systems of linear equations. (English. Russian original) Zbl 1157.15308
J. Math. Sci., New York 155, No. 6, 839-858 (2008); translation from Fundam. Prikl. Mat. 13, No. 4, 67-94 (2007).
Summary: New definitions of determinant functionals over the quaternion skew field are given. The inverse matrix over the quaternion skew field is represented by analogues of the classical adjoint matrix. Cramer’s rules for right and left quaternionic systems of linear equations are obtained.

MSC:
15A15 Determinants, permanents, traces, other special matrix functions
15A06 Linear equations (linear algebraic aspects)
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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