Acute perturbation of Drazin inverse and oblique projectors

Abstract

For an n×n complex matrix A with ind(A) = r; let A^D and A^{\pi } = I-AA^D be respectively the Drazin inverse and the eigenprojection corresponding to the eigenvalue 0 of A: For an n×n complex singular matrix B with ind(B) =s; it is said to be a stable perturbation of A; if I-{(B^{\pi }-A^{\pi })}^{\mathrm{2}} is nonsingular, equivalently, if the matrix B satisfies the condition R(Bs) R(B^s)\cap N(A^r)=\left\{0\right\} and N(B^s)\cap R(A^r)=\left\{0\right\}, introduced by Castro-Gonz

Keywords

Drazin inverse / acute perturbation / stable perturbation / spectral radius / spectral norm / oblique projection

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