Dimitrios Pappas

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In this work we study the numerical range $W(T)$ of EP matrices or operators having a canonical form $T =  U(A\oplus 0)U^* $ in the case when $0 \notin W(A)$. As a result, we define the distance $d(W(A,T))$ between the sets $W(A)$ and $W(T)$ and investigate their connenctions, giving also upper and lower bounds for the distance $d(W(A^{-1},T^\dagger))$.   Finally we present the form of their angular numerical range $F(T)$ and its connection with $F(T^\dagger)$.


Numerical Range, Angular numerical range, EP matrices, Moore-Penrose inverse.

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A. Ben-Israel, T. N. E. Grenville: Generalized Inverses: Theory and Applications, Springer- Verlag,

Berlin, (2002)

S. L. Campbell, C. D. Meyer: Generalized Inverses of Linear Transformations, Dover Publications Inc., New York, (1991)

Drivaliaris D., Karanasios S., Pappas D.:

{em Factorizations of EP operators, }Linear Algebra and Applications,

, 1555-1567 (2008)

C. W. Groetsch, {em Generalized inverses of linear operators,} Marcel Dekker Inc. New York (1977)

K.E. Gustafson and D.K.M. Rao, Numerical Range, Springer, New York (1997)

Hochstenbach M. E., Singer, D. A., Zachlin, P. F.: Numerical approximation of the field of values of the inverse of a large matrix. (CASA-report; Vol. 1308). Eindhoven: Technische Universiteit Eindhoven. (2013)

R. Horn, C. Johnson: Topics in Matrix Analysis, Cambridge Univ. Press (1991)

H. Langer, A. Markus, and C. Tretter: Corners of numerical ranges, Operator Theory: Advances and Applications, 124 , 383-400 (2001)

L. Knockaert: Necessary and sufficient conditions for the origin to belong to the numerical range of a matrix

WSEAS Trans. Math., 5, 1350-1352 (2006)

P. Psarrakos, M. Tsatsomeros: Numerical Range (in) a matrix nutshell, Mathematics Notes (V. 155) Department of Mathematics, Washington State University, (2002)

H. Schwerdtfeger,{em Introduction to Linear Algebra and the Theory of Matrices,} P. Noordhoff,

Groningen, (1950)

Y. Tian: Characterizations of EP matrices and weighted EP matrices, Linear Algebra and its Applications 434(5), 1295-1318 (2011)

DOI: https://doi.org/10.22190/FUMI2004079P


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