Nonlinear matrix algebra and engineering applications Part 2: Polynomial form matrices

Matrix Algebra , Class Notes ( part 2 )

Convention: Let A be a T×m matrix; the notation vec(A) will mean the Tmelement column vector whose first set of T elements are the first colum of A, that is a.1 using the dot notation for columns; the second set of T elements are those of the second column of A, a.2, and so on. Thus A = [a.1, a.2, · · · , a.m] in the dot notation. An immediate consequences of the above Convention is Vec of a pr...

Hurwitz Matrix for Polynomial Matrices

If a system is given by its transfer function then the stability of the system is determined hy the denominator polynomial and its corresponding Hurwitz matrix 7-{. Also the critical stability conditions are determined by its determinant det 7-{. The aim of this paper is to get a generalized Hurwitz matrix for polynomial matrices. In order to achieve that, we first obtain a relation between the...

Computing Popov Form of Ore Polynomial Matrices

We show that the computation of the Popov form of Ore polynomial matrices can be formulated as a problem of computing the left nullspace of such matrices. While this technique is already known for polynomial matrices, the extension to Ore polynomial matrices is not immediate because multiplication of the matrix entries is not commutative. A number of results for polynomial matrices are extended...

Computational Polynomial Algebra and Its Biological Applications

This is an informal note that provides basic information about methods and software tools of resultants, triangular sets, Gröbner bases, real solving, quantifier elimination, and symbolic-numeric computation developed in computational polynomial algebra. Some recent applications of the methods and tools to the study of biological networks are discussed briefly.

Nonnegative matrices, max-algebra and applications