A common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the Weierstrass canonical form. The Weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. The present ...

a common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the weierstrass canonical form. the weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. the present ...

In several applications, e.g., in control and systems modeling theory, Drazin inverses and matrix pencil methods for the study of generalized (descriptor) linear systems are used extensively. In this paper, a relation between the Drazin inverse and the Kronecker canonical form of rectangular pencils is derived and fully investigated. Moreover, the relation between the Drazin inverse and the Wei...

the famous primary and cyclic decomposition theorems along with the tightly related rational and jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.

The Weierstrass curve is a pointed $(X,\infty)$ with numerical semigroup $H_X$, which normalization of the given by canonical form, $y^r + A_{1}(x) y^{r-1} A_{2}(x) y^{r-2} +\dots A_{r-1}(x) y A_{r}(x)=0$ where each $A_j$ polynomial in $x$ degree $\leq j s/r$ for certain coprime positive integers $r$ and $s$, $r$<$s$, such that generators non-gap sequence $H_X$ at $\infty$ include $s$. has ...

We prove that any minimal (maximal) strongly regular surface in the threedimensional Minkowski space locally admits canonical principal parameters. Using this result, we find a canonical representation of minimal strongly regular time-like surfaces, which makes more precise the Weierstrass representation and shows more precisely the correspondence between these surfaces and holomorphic function...

In the present paper, we proposed a new efficient rank updating methodology for evaluating the rank (or equivalently the nullity) of a sequence of block diagonal Toeplitz matrices. The results are applied to a variation of the partial realization problem. Characteristically, this sequence of block matrices is a basis for the computation of the Weierstrass canonical form of a matrix pencil that ...