Abstract.
Matrices of a given size with entries from a field form an associative algebra, and can therefore be considered as a Jordan algebra. From that point of view, the determinant of a matrix is nothing but the reduced generic norm of the Jordan algebra. The basic expansion formulas of matrix determinants along a row or column do not make sense in the setting of arbitrary Jordan algebras. However, there also exists an expansion formula for matrix determinants along the diagonal of a matrix. In the paper, we show that, suitably interpreted, such an expansion formula holds for the reduced generic norm of a large class of Jordan algebras, including separable finite-dimensional Jordan algebras over fields of characteristic not 2.
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Received: 6.8.1996
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Neher, E. An expansion formula for the norm of a Jordan algebra. Arch. Math. 69, 105–111 (1997). https://doi.org/10.1007/s000130050099
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DOI: https://doi.org/10.1007/s000130050099