polynomials

Angles between matrices and between polynomials in fractional linear systems and electrical circuits

The notions of angles between matrices and between polynomials of fractional linear systems and electrical circuits are proposed. In analysis of  angles between state matrices of fractional linear systems the Hadamard product of two matrices  is applied. The angles between matrices and their functions are also addressed. The angles between symmetrical and asymmetrical part of matrices are investigated. The angles between polynomials of transfer matrices of fractional linear systems are analyzed and some new properties are established.

Analysis of measurement systems mathematical models by using the comparison of functions

We propose an approach to mathematical modeling for a system on the basis of comparing scalar products in spaces of real functions integrable on the segment.  This approach may be used in discrete and continuous measurement systems and some combinatorial systems, in which comparison problem of function exists in the process of synthesis and optimal choice of their parameters.  In theory, such problems are characteristic of boundary value problems for equations of mathematical physics, in particular for multi-point problems that describe oscillatory processes in mechanisms.  We have found th