Abstract

In this work a technique to improve the condition number s i of a simple eigenvalue λ i of a matrix A ∈ C n × n is given. This technique obtains a rank one updated matrix that is similar to A with the eigenvalue condition number of λ i equal to one. More precisely, the similar updated matrix A + v i q ∗ , where A v i = λ i v i and q is a fixed vector, has s i = 1 and the remaining condition numbers are at most equal to the corresponding initial condition numbers. Moreover an expression to compute the vector q , using only the eigenvalue λ i and its eigenvector v i , is given.

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