Generalized trace pseudo-spectrum of matrix pencils

Abstract

The objective of the study was to investigate a new notion of generalized trace pseudospectrum 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. RESUMEN El objetivo de este estudio es investigar una nueva noción de pseudo-espectro traza generalizado para pinceles de matrices. En particular, demostramos variadas propiedades nuevas e interesantes del pseudo-espectro traza generalizado. Adicionalmente, mostramos un análogo del teorema espectral de aplicaciones para el pseudo-espectro traza generalizado en elálgebra de matrices.

Utilizing Pseudoinverse Matrix to Solve an Nonlinear Boundary Value Problem

“…The study of different kinds of matrices (for example, matrix pencils, generalized inverse, or Moore-Penrose inverse matrix (pseudoinverse) ) are by now a very thoughtful subject, with the notion of pseudospectrum and pseudoinverse playing a key role in the theory ( for example, perturbation theory, generalized eigenvalue problems theory), see [1][2][3][4][5][6][7].…”