Results 1 to 10 of about 2,762,818 (340)
On the numerical range of an operator [PDF]
Proceedings of the American Mathematical Society, 1963 The numerical range of an operator P in a Hubert space is defined as the set of all the complex numbers (Tx, x), where x is a unit vector in the space. It is well known that a bounded normal operator has the property that the closure of its numerical range is exactly the convex hull of its spectrum [5, pp. 325-327, Theorem 8.13 and Theorem 8.14].
Ching-Hwa Meng
openalex +3 more sources
Product numerical range in a space with tensor product structure [PDF]
Linear Algebra Appl., 434 (2011) 327-342, 2010 We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived.
Bebiano +29 more
arxiv +4 more sources
Semidefinite geometry of the numerical range [PDF]
The Electronic Journal of Linear Algebra, 2010 The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI), an affine ...
Henrion, Didier
core +6 more sources
On the boundary of weighted numerical ranges [PDF]
, 2014 In this article, we are going to introduce the weighted numerical range which is a further generalization both the c-numerical range and the rank k numerical range. If the boundaries of weighted numerical ranges of two matrices (possibly of different sizes) overlap at sufficiently many points, then the two matrices share common generalized eigenvalues.
Cheung, Wai-Shun
arxiv +3 more sources
Numerical shadows: measures and densities on the numerical range [PDF]
Linear Algebra and its Applications, 2010 For any operator $M$ acting on an $N$-dimensional Hilbert space $H_N$ we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numerical range of $M$.
Anderson +28 more
core +4 more sources
A note on convexity of sections of quaternionic numerical range [PDF]
, 2018 The quaternionic numerical range of matrices over the ring of quaternions is not necessarily convex. We prove Toeplitz-Hausdorff like theorem, that is, for any given quaternionic matrix every section of its quaternionic numerical range is convex. We provide some additional equivalent conditions for the quaternionic numerical range of matrices over ...
Kumar, P. Santhosh
arxiv +3 more sources
Numerical range for random matrices [PDF]
Journal of Mathematical Analysis and Applications, 2014 We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. For a large class of random matrices their numerical range is shown to converge to a disc.
Collins, Benoît +3 more
core +4 more sources
On the intrinsic and the spatial numerical range [PDF]
Journal of Mathematical Analysis and Applications, 2005 For a bounded function $f$ from the unit sphere of a closed subspace $X$ of a Banach space $Y$, we study when the closed convex hull of its spatial numerical range $W(f)$ is equal to its intrinsic numerical range $V(f)$.
Facultad De Ciencias +3 more
core +4 more sources
Numerical Range and Quadratic Numerical Range for Damped Systems [PDF]
, 2017 We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations $\ddot{z}(t) + D \dot{z} (t) + A_0 z(t) = 0$ in a Hilbert space.
Jacob, Birgit +3 more
core +3 more sources
The Correlation Numerical Range of a Matrix and Connes' Embedding Problem [PDF]
arXiv, 2011 We define a new numerical range of an n\timesn complex matrix in terms of correlation matrices and develop some of its properties. We also define a related numerical range that arises from Alain Connes' famous embedding problem.
Hadwin, Don, Han, Deguang
arxiv +4 more sources