A new formula of the determinant tensor with symmetries

초록

In this paper, we present a new formula of the determinant tensor detn for n x n matrices. In Ju et al. [Finding tensor decompositions with sparse optimization. J. Korean Math. Soc. 2025; 62(1): 33- 49, doi.org/10.4134/JKMS.j230579], the same authors found a new formula of 4 x 4 determinant tensor det4, which is available when the base field is not of characteristic 2. Considering some symmetries in that formula, we found a new formula so that Crank(detn) = rank(detn) = n!2(n-2)/2 when the base field is not of characteristic 2.

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