Related papers: Partial trace of a full symmetrizer
The goal of this note is to provide a recursive algorithm that allows one to calculate the expansion of the metric tensor up to the desired order in Riemann normal coordinates. We test our expressions up to fourth order and predict results…
We present a rational expression for the trace of the multiplication map M_r in a finite-dimensional algebra of the form A:=K[x_1,...,x_n]/I in terms of the generalized Chow form of I. Here, I is a zero-dimensional ideal of K[x_1,...,x_n]…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant. Copositive tensors have found important applications in polynomial optimization and tensor complementarity…
This paper deals with questions relating to Haghverdi and Scott's notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every partially traced category can be faithfully…
The trace functions for the Parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra $\g$ and any positive integer $k$ are studied and an explicit modular transformation formula of the trace functions is…
Based on some previous results, one gives a general formula for introducing electromagnetic multipole expansions in terms of symmetric and traceless cartesian tensors.
We present some new inequalities related to determinant and trace for positive semidefinite block matrices by using symmetric tensor product, which are extensions of Fiedler-Markham's inequality and Thompson's inequality.
Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…
We investigate the relationship between partial traces and their dilations for general complex matrices, focusing on two main aspects: the existence of (joint) dilations and norm inequalities relating partial traces and their dilations.…
The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of…
We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…
For a 4th order 3-dimensional symmetric tensor with its some entries $1$ or $-1$, we show the analytic sufficient and necessary conditions of its positive definiteness. By applying these conclusions, several strict inequalities is bulit for…
A real symmetric tensor is orthogonally decomposable (or odeco) if it can be written as a linear combination of symmetric powers of $n$ vectors which form an orthonormal basis of $\mathbb R^n$. Motivated by the spectral theorem for real…
Our previous work [1] constructed, in three-dimensional momentum space, a manifestly crossing symmetric basis for scalar conformal four-point functions, based on the factorization property proposed by Polyakov. This work extends this…
The goal of this note is to give, at least for a restricted range of indices, a short proof of homogeneous commutator estimates for fractional derivatives of a product, using classical tools. Both $L^{p}$ and weighted $L^{p}$ estimates can…
We show that the distributions occurring in the geometric and spectral side of the twisted Arthur-Selberg trace formula extend to non-compactly supported test functions. The geometric assertion is modulo a hypothesis on root systems proven…
Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
Given a braided pivotal category $\mathcal C$ and a pivotal module tensor category $\mathcal M$, we define a functor $\mathrm{Tr}_{\mathcal C}:\mathcal M \to \mathcal C$, called the associated categorified trace. By a result of…