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In this paper, we study the perturbation of the extreme singular values of amatrix in the particular case where it is obtained after appending an arbitrarycolumn vector. Such results have many applications in bifurcation theory,signal processing, control theory and many other fields. In the first part ofthis paper, we review and compare various bounds from recent research papers onthis subject. We also present a new lower bound and a new upper bound on theperturbation of the operator norm is provided. Simple proofs are provided,based on the study of the characteristic polynomial rather than on variationalmethods, as e.g. in \cite{Li-Li}. In a second part of the paper, we presentapplications to signal processing and control theory.

Perturbation bounds on the extremal singular values of a matrix after appending a column