Generalized trace pseudo-spectrum of matrix pencils

Abstract

The objective of the study was to investigate a new notion of generalized trace pseudo-spectrum for an matrix pencils. In particular, we prove many new interesting properties of the generalized trace pseudo-spectrum. In addition, we show an analogue of the spectral mapping theorem for the generalized trace pseudo-spectrum in the matrix algebra.

Keywords

• pseudo-spectrum
• condition pseudo-spectrum
• trace pseudo-spectrum