We give a Coulson integral formula and Coulson-Jacobs for the p-Schatten energy of bipartite graphs. use these formulas to compare different trees by using quasiorder, establishing maximality paths minimality stars among all trees.

A compactness criterion for Stieltjes transformation S λ : L 2 → L 2 of the form (1.1) is obtained. The main result is conditions for belonging S λ to Schatten-von Neumann class S p , 0 < p < ∞.

Schatten-IT sind Systeme, Organisationsstrukturen oder Prozesse, die Geschäftsprozesse unterstützen, aber weder technisch noch strategisch ins IT-Service-Management integriert sind. Um in Unternehmen ein Bewusstsein für Schatten-IT zu schaffen, wurde ein Lernspiel entwickelt, welches die Facetten von Schatten-IT spielerisch verdeutlichen soll. In diesem Paper wird der Prototyp dieses Spieles vo...

In this paper, we establish the following perturbation result concerning the singular values of a matrix: Let A,B ∈ R be given matrices, and let f : R+ → R+ be a concave function satisfying f(0) = 0. Then, we have min{m,n}

Understanding the singular value spectrum of a matrix A ∈ Rn×n is a fundamental task in countless numerical computation and data analysis applications. In matrix multiplication time, it is possible to perform a full SVD of A and directly compute the singular values σ1, . . . , σn. However, little is known about algorithms that break this runtime barrier. Using tools from stochastic trace estima...

Let Φ be a super-operator, i.e., a linear mapping of the form Φ : L(F) → L(G) for finite dimensional Hilbert spaces F and G. This paper considers basic properties of the super-operator norms defined by ‖Φ‖q→p = sup{‖Φ(X)‖p/‖X‖q : X 6= 0}, induced by Schatten norms for 1 ≤ p, q ≤ ∞. These super-operator norms arise in various contexts in the study of quantum information. In this paper it is prov...

Let $A=U|A|$ be the polar decomposition of an operator $A$ on a Hilbert space $mathscr{H}$ and $lambdain(0,1)$. The $lambda$-Aluthge transform of $A$ is defined by $tilde{A}_lambda:=|A|^lambda U|A|^{1-lambda}$. In this paper we show that emph{i}) when $mathscr{N}(|A|)=0$, $A$ is self-adjoint if and only if so is $tilde{A}_lambda$ for some $lambdaneq{1over2}$. Also $A$ is self adjoint if and onl...

Two–sided estimates of Schatten–von Neumann norms for weighted Volterra integral operators are established. Analogous problems for some potential-type operators defined on R are solved. Let H be a separable Hilbert space and let σ∞(H) be the class of all compact operators T : H → H, which forms an ideal in the normed algebra B of all bounded linear operators onH. To construct a Schattenvon Neum...

Although K-Means clustering has been widely studied due to its simplicity, these methods still have the following fatal drawbacks. Firstly, they need initialize cluster centers, which causes unstable performance. Secondly, poor performance on non-Gaussian datasets. Inspired by affinity matrix, we propose a novel multi-view based adjacency matrix. It maps matrix distance according principle that...