相关论文: A New Form of Williamson's Product Theorem

In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…

In this pedagogical note I present the operator form of Wick's theorem, i.e. a procedure to bring a product of 1-particle creation and destruction operators to normal order, with respect to some reference many-body state. Both the static…

We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. Then, we study the abundance of…

We establish a Liouville type theorem for some conformally invariant fully nonlinear equations

The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.

We prove a formula expressing the $K$-theoretic log Gromov-Witten invariants of a product of log smooth varieties $V \times W$ in terms of the invariants of $V$ and $W$. The proof requires introducing log virtual fundamental classes in…

The variety of uniform matrix product states arises both in algebraic geometry as a natural generalization of the Veronese variety, and in quantum many-body physics as a model for a translation-invariant system of sites placed on a ring.…

We generalize Bourgain's discretized sum-product theorem to matrix algebras.

We establish a Pythagorean theorem for the absolute values of the blocks of a partitioned matrix. This leads to a series of remarkable operator inequalities.

In the present paper we prove Liouville-type theorems: non-existence theorems for complete twisted and warped products of Riemannian manifolds which generalize and complement similar results for compact manifolds.

We introduce a new matrix product, that we call the wreath product of matrices. The name is inspired by the analogous product for graphs, and the following important correspondence is proven: the wreath product of the adjacency matrices of…

A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related…

We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…

It is shown that a $N\times N$ real symmetric [complex hermitian] positive definite matrix $V$ is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in $SO(m,n)$ [ $SU(m,n)$], for any choice of partition…

We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally decomposed as a product manifold…

A theorem of Thompson provides a non-self-adjoint variant of the classical Schur-Horn theorem by characterizing the possible diagonal values of a matrix with given singular values. We prove an analogue of Thompson's theorem for II_1…

We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…

In this paper we present theorems and applications of Wallis theorem related to trigonometric integrals.

The absolute value of matrices is used in order to give inequalities for the trace of products. An application gives a very short proof of the tracial matrix Hoelder inequality

The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments…