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The results of [I. Ojeda, Amer. Math. Monthly, 122, pp 60--64] provides a characterization of Kronecker square roots of matrices in terms of the symmetry and rank of the block vec matrix (rearrangement matrix). In this short note we reformulate the characterization in terms of rank only by considering an alternative to the block vec matrix, provided that the characteristic of the underlying field is not equal to 2.
Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a solution i
Let $det_2(A)$ be the block-wise determinant (partial determinant). We consider the condition for completing the determinant $det(det_2(A)) = det(A),$ and characterize the case for an arbitrary Kronecker product $A$ of matrices over an arbitrary fiel
In this work, we present a standard model for Galois rings based on the standard model of their residual fields, that is, a sequence of Galois rings starting with ${mathbb Z}_{p^r} that coves all the Galois rings with that characteristic ring and suc
We provide a formula for commputing the discriminant of skew Calabi-Yau algebra over a central Calabi-Yau algebra. This method is applied to study the Jacobian and discriminant for reflection Hopf algebras.
The aim of this paper is to study linear preservers of the trace of Kronecker sums and their connection with preservers of determinants of Kronecker products. The partial trace and partial determinant play a fundamental role in characterizing the pre