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Determinants for nxn matrices and the symmetric Newton formula in the 3x3 case

One of the aims of this paper is to provide a short survey on the Z2-graded, the symmetric and the left (right) generalizations of the classical determinant theory for square matrices with entries in an arbitrary (possibly non-commutative) ring. This will put us in a position to give a motivation for our main results. We use the preadjoint matrix to exhibit a general trace expression for the symmetric determinant. The symmetric version of the classical Newton trace formula is also presented in the 3x3 case.

preprint2015arXivOpen access
J. SzigetiL. van Wyk
math.RA
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J. SzigetiL. van Wyk

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