theorem on the spectral decomposition of normal matrices

On the stable determination of some earth's radial density models

The regulanzation algorithm was developed on the basis of such Jit of the normal operator which is closed to a system of linear equations with scalar or unit matrix. The application of the famous theorem on the spectral expansion of normal matrixes Jed to introducing of the simplest matrix norm (connected with the traditional Euclidean norm) and allowed form special condition, which provides the determination of the regulanzation parameter.