ترغب بنشر مسار تعليمي؟ اضغط هنا

Preserving the trace of the Kronecker sum

68   0   0.0 ( 0 )
 نشر من قبل Yorick Hardy
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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 preservers of the trace of Kronecker sums and preservers of the determinant of Kronecker products respectively.



قيم البحث

اقرأ أيضاً

101 - Yorick Hardy 2017
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 d. Further insisting that $det_2(AB)=det_2(A)det_2(B)$, for Kronecker products $A$ and $B$, yields a multiplicative monoid of matrices. This leads to a determinant-root operation $text{Det}$ which satisfies $text{Det}(text{Det}_2(A)) = text{Det}(A)$ when $A$ is a Kronecker product of matrices for which $text{Det}$ is defined.
87 - Yorick Hardy 2015
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 c haracterization 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.
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(x^j). Such an expression can be naturally evaluated on matrices, where the trace symbols are evaluated as normalized traces. This paper addresses global and con strained positivity of univariate trace polynomials on symmetric matrices of all finite sizes. A tracial analog of Artins solution to Hilberts 17th problem is given: a positive semidefinite univariate trace polynomial is a quotient of sums of products of squares and traces of squares of trace polynomials.
Let $A$ be an algebra and let $f(x_1,...,x_d)$ be a multilinear polynomial in noncommuting indeterminates $x_i$. We consider the problem of describing linear maps $phi:Ato A$ that preserve zeros of $f$. Under certain technical restrictions we solve t he problem for general polynomials $f$ in the case where $A=M_n(F)$. We also consider quite general algebras $A$, but only for specific polynomials $f$.
In this paper, we study the metric geometric mean introduced by Pusz and Woronowicz and the spectral geometric mean introduced by Fiedler and Ptak, originally for positive definite matrices. The relation between $t$-metric geometric mean and $t$-spec tral geometric mean is established via log majorization. The result is then extended in the context of symmetric space associated with a noncompact semisimple Lie group. For any Hermitian matrices $X$ and $Y$, Sos matrix exponential formula asserts that there are unitary matrices $U$ and $V$ such that $$e^{X/2}e^Ye^{X/2} = e^{UXU^*+VYV^*}.$$ In other words, the Hermitian matrix $log (e^{X/2}e^Ye^{X/2})$ lies in the sum of the unitary orbits of $X$ and $Y$. Sos result is also extended to a formula for adjoint orbits associated with a noncompact semisimple Lie group.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا