If E = {ei} and F = {fi} are two 1-unconditional basic sequences in L1 with E r-concave and F p-convex, for some 1 ≤ r < p ≤ 2, then the space of matrices {ai,j} with norm ∥{ai,j}∥E(F ) = ∥∥∑ k ∥ ∑ l ak,lfl∥ek ∥∥ embeds into L1. This generalizes a recent result of Prochno and Schütt.

In this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the Hermitian matrix expression $$‎ ‎f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is‎ ‎Hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$X$ and $Y$ satisfy‎ ‎the following consistent system of matrix equations $A_{3}Y=C_{3}‎, ‎A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As‎ ‎consequences‎, ‎we g...

a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...

matrix metalloproteinases (mmps) are a family of neutral proteinases that are important in normal development, cellular differentiation or migration, angiogenesis, neurogenesis, wound repair, and a wide range of pathological processes such as oxidative stress and neuroinflammation. mmps have been demonstrated to increase the permeability of the blood–brain barrier (bbb) by degrading the compone...

We consider the c = 1 matrix model deformed by the operator 2M TrΦ −2, which was conjectured by Jevicki and Yoneya to describe a two-dimensional black hole of mass M . We calculate the exact non-perturbative S-matrix and show that all the amplitudes involving an odd number of particles vanish at least to all orders of perturbation theory. We conjecture that these amplitudes vanish non-perturbat...

the star-mesh transformation allows the reduction of nodes in an electrical circuit. the gauss elimination method allows the reduction of unknowns in a system of linear equations . triangular decomposition can be used to find the inverse of a matrix. in this paper the coherence between these methods are discussed. it is shown that the gauss elimination method gives the same formula for star-mes...