On the Block Numerical Range of Nonnegative Matrices

2008 ◽  
pp. 113-133 ◽  
Author(s):  
K.-H. Förster ◽  
N. Hartanto
Keyword(s):  
Numerical Range ◽  
Nonnegative Matrices

scholarly journals The higher rank numerical range of nonnegative matrices

2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Aikaterini Aretaki ◽  
Ioannis Maroulas
Keyword(s):  
Complex Plane ◽  
Numerical Range ◽  
Nonnegative Matrix ◽  
Maximum Modulus ◽  
Companion Matrix ◽  
Nonnegative Matrices ◽  
Higher Rank

AbstractIn this article the rank-k numerical range ∧k (A) of an entrywise nonnegative matrix A is investigated. Extending the notion of elements of maximum modulus in ∧k (A), we examine their location on the complex plane. Further, an application of this theory to ∧k (L(λ)) of a Perron polynomial L(λ) is elaborated via its companion matrix C L.

Nonnegative Matrices and Applications

1997 ◽  
Author(s):  
R. B. Bapat ◽  
T. E. S. Raghavan
Keyword(s):  
Nonnegative Matrices

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.

Continuity of submatrices and Ritz sets associated to a point in the numerical range

2021 ◽  
Vol 624 ◽  
pp. 1-13
Author(s):  
Kennett L. Dela Rosa ◽  
Hugo J. Woerdeman
Keyword(s):  
Numerical Range

scholarly journals The Global Convergence of the Nonlinear Power Method for Mixed-Subordinate Matrix Norms

2021 ◽  
Vol 88 (1) ◽  
Author(s):  
Antoine Gautier ◽  
Matthias Hein ◽  
Francesco Tudisco
Keyword(s):  
Global Convergence ◽  
Convergence Theorem ◽  
Matrix Norm ◽  
Nonnegative Matrices ◽  
Np Hard ◽  
Power Method ◽  
Contraction Ratio ◽  
Matrix Norms ◽  
Vector Norms

AbstractWe analyze the global convergence of the power iterates for the computation of a general mixed-subordinate matrix norm. We prove a new global convergence theorem for a class of entrywise nonnegative matrices that generalizes and improves a well-known results for mixed-subordinate $$\ell ^p$$ ℓ p matrix norms. In particular, exploiting the Birkoff–Hopf contraction ratio of nonnegative matrices, we obtain novel and explicit global convergence guarantees for a range of matrix norms whose computation has been recently proven to be NP-hard in the general case, including the case of mixed-subordinate norms induced by the vector norms made by the sum of different $$\ell ^p$$ ℓ p -norms of subsets of entries.

a-Numerical range on $$C^*$$-algebras

Positivity ◽  
2021 ◽  
Author(s):  
Abdellatif Bourhim ◽  
Mohamed Mabrouk
Keyword(s):  
Numerical Range ◽  
C Algebras

On the maximal numerical range of the bimultiplication M2,A,B

2021 ◽  
pp. 1-8
Author(s):  
Abderrahim Baghdad ◽  
Chraibi Kaadoud Mohamed
Keyword(s):  
Numerical Range

scholarly journals On the similarity to nonnegative and Metzler Hessenberg forms

2021 ◽  
Vol 10 (1) ◽  
pp. 1-8
Author(s):  
Christian Grussler ◽  
Anders Rantzer
Keyword(s):  
Standard Form ◽  
Complete Characterization ◽  
Nonnegative Matrices ◽  
Positive Systems ◽  
Third Order ◽  
Hessenberg Form ◽  
Hessenberg Matrices ◽  
Open Question ◽  
Order Continuous

Abstract We address the issue of establishing standard forms for nonnegative and Metzler matrices by considering their similarity to nonnegative and Metzler Hessenberg matrices. It is shown that for dimensions n 3, there always exists a subset of nonnegative matrices that are not similar to a nonnegative Hessenberg form, which in case of n = 3 also provides a complete characterization of all such matrices. For Metzler matrices, we further establish that they are similar to Metzler Hessenberg matrices if n 4. In particular, this provides the first standard form for controllable third order continuous-time positive systems via a positive controller-Hessenberg form. Finally, we present an example which illustrates why this result is not easily transferred to discrete-time positive systems. While many of our supplementary results are proven in general, it remains an open question if Metzler matrices of dimensions n 5 remain similar to Metzler Hessenberg matrices.

scholarly journals $L$-ideals and numerical range preservation

1977 ◽  
Vol 21 (2) ◽  
pp. 365-373 ◽  
Author(s):  
C. K. Chui ◽  
P. W. Smith ◽  
R. R. Smith ◽  
J. D. Ward
Keyword(s):  
Numerical Range
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