On Hölder condition numbers

A matrix with complex elements is considered. An algebraic method to find the maximum order of matrix Jordan block is suggested. The polynomial whose roots are the eigenvalues that correspond to the maximum Jordan block is constructed. The algorithm does not require the knowledge of the Jordan form of the matrix and its characteristic polynomial. It is based on finding Jordan blocks corresponding to the eigenvalue 0 of the other matrix, constructed with the help of Kronecker product. The results presented could be used for calculating the Hölder condition number which is the measure of the eigenvalue variation as small variations of matrix elements. Bibliogr. 7.