Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 2, pp. 215-225 (2015)

Localization of the pseudospectra of matrices through the numerical range

Abdelkader Frakis and Abderrahmane Smail

University of Mascara and University of Oran

Abstract: Numerical range and pseudospectra of a matrix play an important role in different areas and have several applications in different domains. The numerical range gives an estimate to the location of the pseudospectra, the present work proposes some properties of pseudospectra of a matrix and provides a connection between numerical range and pseudospectra of a matrix. Some upper bounds for pseudospectra of a matrix are given. Also we use the pseudospectra to solve a problem concerning the matrices which are nearly commuting.

Keywords: Pseudospectra, numerical range, numerical positive abscissa, numerical negative abscissa, pseudoprojection, almost commuting matrices.

Classification (MSC2000): 15A18; 15A60, 15A42, 15A27, 65F15, 65F35

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