Results 301 to 310 of about 2,436,536 (336)

Normality and the Higher Numerical Range

Canadian Journal of Mathematics, 1978
Let Mn(C) be the vector space of all w-square complex matrices. Denote by (• , •) the standard inner product in the space C n of complex n-tuples. For a matrix A ∈ Mn(C) and an n-tuple c = (c1,…
Marcus, Marvin, Moyls, Benjamin N., Filippenko, Ivan   +2 more
openaire   +1 more source

On a Family of Generalized Numerical Ranges

Canadian Journal of Mathematics, 1974
Throughout this note, an operator will always mean a bounded linear operator acting on a Hilbert space X into itself, unless otherwise stated. The class Cρ (0 < ρ < ∞ ) of operators, considered by Sz.-Nagy and Foiaş [5], is defined as follows: An operator T is in Cρ if Tnx = pPUnx for all x ∊ X, n = 1, 2, . . .
openaire   +1 more source

Convexity of the Joint Numerical Range

SIAM Journal on Matrix Analysis and Applications, 2000
Let \(A=(A_1,\ldots,A_m)\) be an \(m\)-tuple of \(n\times n\) Hermitian matrices. For \(1\leq k\leq n,\) the \(k\)th joint numerical range of \(A\) is defined as \[ W_k(A)=\{(\text{tr}(X^\star A_1X),\dots,\text{tr}(X^\star A_mX))\mid X\in{\mathbb{C}}^{n\times k},X^\star X=I_k\}. \] The authors pose a number of problems, e.g.
Li, Chi-Kwong, Poon, Yiu-Tung
openaire   +2 more sources

Ratio Numerical Ranges of Operators

Integral Equations and Operator Theory, 2011
Let \(H\) be a Hilbert space and \(L(H)\) the algebra of bounded linear operators on \(H\). For \(A\in L(H)\), the numerical range of \(A\) is given by \(W(A)= \{\langle Ax,x\rangle:x\in H,\;\langle x,x\rangle=1\}\). For \(A,B\in L(H)\), \(B\neq 0\), define the ratio numerical range \[ W(A/B)=\left\{\frac{\langle Ax,x\rangle}{\langle Bx,x\rangle}:x\in ...
Rodman, Leiba, Spitkovsky, Ilya M.
openaire   +1 more source

Compressions and Dilations of Numerical Ranges

SIAM Journal on Matrix Analysis and Applications, 1999
The authors continue their study of the numerical range \(\text{NR} [A]\) of an \(n\times n\) complex matrix \(A\). They express \(\text{NR} [A]\) as the union of the numerical ranges of \(k\times k\) matrices for \(2\leq k< n\). In this way each set in the union can be considered as a dilation of \(\text{NR} [A]\). They also consider compressions of \(
Maroulas, J., Adam, M.
openaire   +1 more source

The evolving landscape of salivary gland tumors

Ca-A Cancer Journal for Clinicians, 2023
Conor Steuer
exaly  

Fuel cells with an operational range of –20 °C to 200 °C enabled by phosphoric acid-doped intrinsically ultramicroporous membranes

Nature Energy, 2022
Hongying Tang, Lei Wu, Junjie Liu
exaly  

Numerical Range

1997
Karl E. Gustafson, Duggirala K. M. Rao
openaire   +2 more sources

The numerical range

2023
openaire   +1 more source

Direct observation of chemical short-range order in a medium-entropy alloy

Nature, 2021
Xuefei Chen, Qi Wang, Zhiying Cheng
exaly