Vladimir Sergeichuk
Institute of Mathematics, Academy of Science, Ukraine
Miniversal deformations.
Abstract: The reduction of a matrix to its Jordan form is an unstable operation: if we slightly change a matrix, then its Jordan form may change significantly. Therefore, if the elements of a matrix are known only approximately, then it is unwise to reduce it to its Jordan form. Vladimir Arnold in 1971 constructed a normal form of a matrix A for similarity that slightly changes if the matrix A is slightly changed. He called it a miniversal deformation of A. I will talk about Arnold's miniversal deformations of matrices and their extensions to matrix pencils and matrices of bilinear and sesquilinear forms.