Mixed, Componentwise Condition Numbers and Small Sample Statistical Condition Estimation for Generalized Spectral Projections and Matrix Sign Functions

The explicit expressions of mixed and componentwise condition numbers for the spectral projections, generalized spectral projections and sign functions for matrices and regular matrix pairs are derived. The condition numbers improve some known results of the normwise type and reveal the structured perturbations. Statistical condition estimation is applied to these problems which can be calculated efficiently. 2010Mathematics Subject Classification. 15A18, 15A22, 65F15. Key words and phrases. Mixed, Componentwise, Condition number, Generalized spectral projections, Structured perturbations, Matrix sign functions, Matrix regular pair, Statistical condition estimation.