Results 41 to 50 of about 1,268 (93)

The perturbation of Drazin inverse and dual Drazin inverse

Special Matrices
In this study, we derive the Drazin inverse (A+εB)D{\left(A+\varepsilon B)}^{D} of the complex matrix A+εBA+\varepsilon B with Ind(A+εB)>1{\rm{Ind}}\left(A+\varepsilon B)\gt 1 and Ind(A)=k{\rm{Ind}}\left(A)=k and the group inverse (A+εB)#{\left(A ...
Wang Hongxing, Cui Chong, Wei Yimin
doaj   +1 more source

Multiplicative inequalities for weighted arithmetic and harmonic operator means

Acta Universitatis Sapientiae: Mathematica, 2019
In this paper we establish some multiplicative inequalities for weighted arithmetic and harmonic operator means under various assumption for the positive invertible operators A, B.
Dragomir Sever S.
doaj   +1 more source

THE GROTHENDIECK CONSTANT IS STRICTLY SMALLER THAN KRIVINE’S BOUND

Forum of Mathematics, Pi, 2013
The (real) Grothendieck constant ${K}_{G} $ is the infimum over those $K\in (0, \infty )$ such that for every $m, n\in \mathbb{N} $ and every $m\times n$ real matrix $({a}_{ij} )$ we have $$\begin{eqnarray*}\displaystyle \max _{\{ x_{i}\} _{i= 1}^{m} , \{
MARK BRAVERMAN, KONSTANTIN MAKARYCHEV, YURY MAKARYCHEV, ASSAF NAOR   +3 more
doaj   +1 more source

A 3x3 dilation counterexample

, 2012
We define four 3x3 commuting contractions which do not dilate to commuting isometries. However they do satisfy the scalar von Neumann inequality. These matrices are all nilpotent of order 2.
Choi, Man Duen, Davidson, Kenneth R.
core   +1 more source

Explicit inverse of symmetric, tridiagonal near Toeplitz matrices with strictly diagonally dominant Toeplitz part

Special Matrices
Let Tn=tridiag(−1,b,−1){T}_{n}={\rm{tridiag}}\left(-1,b,-1), an n×nn\times n symmetric, strictly diagonally dominant tridiagonal matrix (∣b∣>2| b| \gt 2). This article investigates tridiagonal near-Toeplitz matrices T˜n≔[t˜i,j]{\widetilde{T}}_{n}:= \left[
Kurmanbek Bakytzhan, Erlangga Yogi, Amanbek Yerlan   +2 more
doaj   +1 more source

Concrete minimal 3 × 3 Hermitian matrices and some general cases

Demonstratio Mathematica, 2017
Given a Hermitian matrix M ∈ M3(ℂ) we describe explicitly the real diagonal matrices DM such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ), where ║ · ║ denotes the operator norm.
Klobouk Abel H., Varela Alejandro
doaj   +1 more source

Finite Sections of Weighted Hardy's Inequality [PDF]

arXiv, 2007
We study finite sections of weighted Hardy's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.
arxiv  

Matrix subadditivity inequalities and block-matrices [PDF]

arXiv, 2008
Several subadditivity results and conjectures are given for matrices (or operators), block-matrices, concave functions and norms.
arxiv  

On the norms of r-circulant matrices with generalized bi-periodic Fibonacci numbers [PDF]

arXiv, 2021
In this paper, we give upper and lower bounds for the spectral norms of r-circulant matrices with the generalized bi-periodic Fibonacci numbers. Moreover, we investigate the eigenvalues and determinants of these matrices.
arxiv  

On the Harmonic and Hyperharmonic Fibonacci Numbers

, 2015
In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which is finite sums
Kesim, Seyhun, Kızılateş, Can, Tuglu, Naim   +2 more
core   +1 more source