Results 1 to 10 of about 2,500,610 (287)

High numerical aperture holographic microscopy reconstruction with extended z range [PDF]

, 2015
An holographic microscopy reconstruction method compatible with high numerical aperture microscope objective (MO) up to NA=1.4 is proposed. After off axis and reference field curvature corrections, and after selection of the +1 grating order holographic ...
Donnarumma, Dario, Gross, Michel, Tessier, Gilles, Verrier, Nicolas   +3 more
core   +4 more sources

On generalized numerical ranges [PDF]

Pacific Journal of Mathematics, 1976
which ||(T- viyι\\ = l/d(υ, W(T)), v£ CLW(T), where CLW(T) is the closure of the numerical range W(T) of Γ, has been generalized by using the concept of generalized numerical ranges due to C. S. Lin. Also it has been shown that the notions of generalized Minkowski distance functionals and generalized numerical ranges arise in a natural way for elements
openaire   +3 more sources

Polynomials and Numerical Ranges [PDF]

Proceedings of the American Mathematical Society, 1988
Let A A be an n × n n \times n complex matrix. For 1 ≤ k ≤ n 1 \leq k \leq n we study the inclusion relation for the following polynomial sets related to the matrix A A . (a) The classical numerical range of the k
openaire   +1 more source

Some results on Drazin-Dagger matrices, reciprocal matrices, and conjugate EP matrices [PDF]

Journal of Mahani Mathematical Research
In this paper, a class of matrices, namely, Drazin-dagger matrices, in which the Drazin inverse andthe Moore-Penrose inverse commute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated.
Mahdiyeh Mortezaei, Gholamreza Aghamollaei   +1 more
doaj   +1 more source

New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal

Demonstratio Mathematica, 2021
A new class of operators, larger than ∗\ast -finite operators, named generalized ∗\ast -finite operators and noted by Gℱ∗(ℋ){{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }}) is introduced, where: Gℱ∗(ℋ)={(A,B)∈ℬ(ℋ)×ℬ(ℋ):∥TA−BT∗−λI ...
Messaoudene Hadia, Mesbah Nadia
doaj   +1 more source

Numerical Range of Moore–Penrose Inverse Matrices

Mathematics, 2020
Let A be an n-by-n matrix. The numerical range of A is defined as W ( A ) = { x * A x : x ∈ C n , x * x = 1 } . The Moore–Penrose inverse A + of A is the unique matrix satisfying A A + A = A , A + A A + = A ...
Mao-Ting Chien
doaj   +1 more source

Volterra operator norms : a brief survey

Moroccan Journal of Pure and Applied Analysis, 2023
In this expository article, we discuss the evaluation and estimation of the operator norms of various functions of the Volterra operator.
Ransford Thomas
doaj   +1 more source

Inverse Numerical Range and Determinantal Quartic Curves

Mathematics, 2020
A hyperbolic ternary form, according to the Helton–Vinnikov theorem, admits a determinantal representation of a linear symmetric matrix pencil. A kernel vector function of the linear symmetric matrix pencil is a solution to the inverse numerical range ...
Mao-Ting Chien, Hiroshi Nakazato
doaj   +1 more source

On some reciprocal matrices with elliptical components of their Kippenhahn curves

Special Matrices, 2021
By definition, reciprocal matrices are tridiagonal n-by-n matrices A with constant main diagonal and such that ai,i+1ai+1,i= 1 for i = 1, . . ., n − 1.
Jiang Muyan, Spitkovsky Ilya M.
doaj   +1 more source

Generalization of numerical range of polynomial operator matrices

Tikrit Journal of Pure Science, 2023
Suppose that  is a polynomial matrix operator where  for , are  complex matrix and let  be a complex variable. For an  Hermitian matrix , we define the -numerical range of polynomial matrix of  as , where .
Darawan Zrar Mohammed, Ahmed Muhammad
doaj   +1 more source