In Part I we proposed a multilinear algebra framework to solve 0-dimensional systems of polynomial equations with simple roots. We extend this incorporate multiple roots: block term decomposition (BTD) the null space Macaulay matrix reveals dual (sub)space disjoint root in each term. The BTD is joint triangularization multiplication tables and three-way generalization Jordan canonical form case...

I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying pairs (A,B) commuting nilpotent operators on a vector space contains an arbitrary t-tuple linear operators. Moreover, it representations quiver finite-dimensional algebra, so is considered as hopeless. If such pair, then KerA?KerB?0. We give simple normal form (Anor,Bnor) matrices if KerA?KerB one-dimensional. do not ...

We show an explicit formula, with a quite easy deduction, for the exponential matrix $e^{tA}$ of real and finite square $A$ (and complex ones also). The elementary method developed avoids Jordan canonical form, eigenvectors, resolution any linear system, inversion, polynomial interpolation, integration, functional analysis, generalized Fibonacci sequences. basic tools are Cayley-Hamilton theore...

The structure group and the involutive differential system that characterize the pseudo-group of contact transformations on a jet space are determined.

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 ...

We show that an arbitrary Hankel matrix of a nite rank admits a Vandermonde decomposition: H = V T DV , where V is a con-uent Vandermonde matrix and D is a block diagonal matrix. This result was rst derived by Vandevoorde; our contribution here is a presentation that uses only linear algebra, speciically, the Jordan canonical form. We discuss the choices for computing this decomposition in only...

Abstract: The paper considers the problem of virtual sensor design for nonlinear dynamic systems with non-smooth nonlinearities described by continuous-time models faulty physical replacement. It is assumed that to solve problem, system equipped diagnostic allowing detecting and isolating sensor. For every such a sensor, generating estimate replacing designed. To so-called logic-dynamic approac...

We present a constructive existence proof that every real skew-Hamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasi-Jordan canonical form via symplectic similarity. We show further that every W has infinitely many real Hamiltonian square roots, and give a lower bound on the dimension of the set of all suc...