A Note on the Level Sets of a Matrix Polynomial and Its Numerical Range

2002 ◽  
pp. 277-281
Author(s):  
Panayiotis J. Psarrakos
Keyword(s):  
Level Sets ◽  
Matrix Polynomial ◽  
Numerical Range

On the rank-k numerical range of matrices polynomials

2014 ◽  
Vol 27 ◽  
Author(s):  
Aik. Aretaki ◽  
John Maroulas
Keyword(s):  
Matrix Polynomial ◽  
Numerical Range ◽  
Complex Matrices ◽  
Geometric Properties

This article introduces the notion of the rank-$k$ numerical range $\Lambda_{k}(L)$ of a matrix polynomial $L(\lambda) = A_{m} \lambda^{m} + \cdots + A_{1} \lambda + A_{0}$, whose coefficients are $n\times n$ complex matrices. Also, geometric properties are obtained, including the relation to the ordinary numerical range $W(L)$.

scholarly journals Point equation of the boundary of the numerical range of a matrix polynomial

2002 ◽  
Vol 347 (1-3) ◽  
pp. 205-217 ◽  
Author(s):  
Mao-Ting Chien ◽  
Hiroshi Nakazato ◽  
Panayiotis Psarrakos
Keyword(s):  
Matrix Polynomial ◽  
Numerical Range ◽  
Point Equation

The C-numerical range of perturbations matrix polynomials

2016 ◽  
Vol 09 (02) ◽  
pp. 1650046 ◽  
Author(s):  
Yaser Jahanshahi ◽  
Bahmann Yousefi
Keyword(s):  
Lower Bound ◽  
Complex Plane ◽  
Matrix Polynomial ◽  
Numerical Range ◽  
Connected Components ◽  
Matrix Polynomials ◽  
Polynomial Formula

In this paper, the [Formula: see text]-radius stability of a matrix polynomial [Formula: see text] relative to a domain [Formula: see text] of the complex plane and its relation with the [Formula: see text]-numerical range of [Formula: see text] are investigated. By using an expression of the [Formula: see text]-radius stability, we obtain a lower bound which involves the distance of [Formula: see text] from the connected components of the [Formula: see text]-numerical range of [Formula: see text].

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

Perfect level sets in many directions

1986 ◽  
Vol 12 (1) ◽  
pp. 176
Author(s):  
Malý
Keyword(s):  
Level Sets

LEVEL SETS OF A TYPICAL C n FUNCTION

1998 ◽  
Vol 24 (1) ◽  
pp. 83
Author(s):  
Darji ◽  
Morayne
Keyword(s):  
Level Sets
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