Let α1, α2, . . . , αn, β1, β2, . . . , βn be strictly positive reals with α1 +α2 + · · ·+αn = β1 + β2 + · · ·+ βn = s. In this paper, the inequality |||Aα1Bβ1Aα2 · · ·AαnBβn ||| ≤ |||AB|||s when A and B are positive-definite matrices is studied. Related questions are also studied.

We aim here at characterizing those nonnegative matrices whose inverse is an irreducible Stieltjes matrix. Specifically, we prove that any irreducible Stieltjes matrix is a resistive inverse. To do this we consider the network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite Schrödinger operator which ground state is determined by the lowest ...

This paper investigates the uniqueness of a nonnegative vector solution and the uniqueness of a positive semidefinite matrix solution to underdetermined linear systems. A vector solution is the unique solution to an underdetermined linear system only if the measurement matrix has a row-span intersecting the positive orthant. Focusing on two types of binary measurement matrices, Bernoulli 0-1 ma...

Let K be a closed convex cone with dual K∗ in a finite-dimensional real Hilbert space V . A positive operator on K is a linear operator L on V such that L (K) ⊆ K. Positive operators generalize the nonnegative matrices and are essential to the Perron-Frobenius theory. We say that L is a Z-operator on K if 〈L (x), s〉 ≤ 0 for all (x, s) ∈ K ×K such that 〈x, s〉 = 0. The Z-operators are generalizat...

We extend some inequalities for normal matrices and positive linear maps related to the Russo-Dye theorem. The results cover case of on a von Neumann algebra mapping any nonzero operator an unbounded operator.

Let H(d) be the space of complex hermitian matrices of size d×d and let H+(d) ⊂ H(d) be the cone of positive semidefinite matrices. A linear operator Φ : H(d1) → H(d2) is said to be positive if Φ[H+(d1)] ⊂ H+(d2). The concurrence C(Φ; ·) of a positive operator Φ : H(d1) → H(d2) is a real-valued function on the cone H+(d1), defined as the largest convex function which coincides with 2 q σ d2 2 (...

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

Inspired by the recent results in [4] and the concept of metric adjusted skew information introduced by Hansen in [6], we here give a further generalization for Schrödinger-type uncertainty relation applying metric adjusted correlation measure introduced in [6]. We firstly give some notations according to those in [4]. Let Mn(C) and Mn,sa(C) be the set of all n × n complex matrices and all n × ...