AN EXPANSION FORMULA FOR THE NORM OF A JORDAN ALGEBRA

Matrices of a given size with entries from a field form an associative algebra, and can therefore be considered as a Jordan algebra. From th at point of view, the determinant of a matrix is nothing but the reduc ed generic norm of the Jordan algebra. The basic expansion formulas of matrix determinants along a row or column do not make sense in the se tting of arbitrary Jordan algebras. However, there also exists an expa nsion formula for matrix determinants along the diagonal of a matrix. In the paper, we show that, suitably interpreted, such an expansion fo rmula holds for the reduced generic norm of a large class of Jordan al gebras, including separable finite-dimensional Jordan algebras over fi elds of characteristic not 2.