ИСТИНА

Linear structures in matrices are described by linear algebraic equations. Typical examples are various kinds of sparsity, included bandedness, and Toeplitz and Hankel matrices. Multiplication and inversion of such matrices generally leads to matrices with polynomial (multilinear) relations between their elements. Other typical examples of multilinear structure are Cauchy and Vandermonde matrices, rank structures and various tensor decompositions. In this talk we survey general results and outline some open research questions for most popular and pervasive linear and multilinear structures.