A Matrix Euclidean Algorithm induced by State Space Realization

Bi-Gyrogroup: The Group-Like Structure Induced by Bi-Decomposition of Groups

‎The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B ‎and a subgroup $H$ of $Gamma$ induces‎, ‎under general conditions‎, ‎a ‎group-like structure for B‎, ‎known as a gyrogroup‎. ‎The famous‎ concrete realization of a gyrogroup‎, ‎which motivated the emergence ‎of gyrogroups into the mainstream‎, ‎is the space of all ‎relativistically admissible velocities along with a binary ‎mbox{...

Matrix factorization and minimal state space realization in the max-plus algebra

The topics of this paper are matrix factorizations and the minimal state space realization problem in the maxplus algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We present a heuristic algorithm to compute a factorization of a matrix in the max-plus algebra. Next we use this algorithm to determine the minimal system order (and to construct a mi...

A matrix Euclidean algorithm for minimal partial realization

Large Matrix Inversion using State Space Techniques

A new computational technique is presented by which large structured matrices can be inverted. The specified matrix is viewed as the input-output operator of a time-varying system. Recently developed state space algorithms which apply to such systems are then used to compute a QR factorization first and subsequently the inverse of the matrix, starting from a state realization of the matrix. The...

Tangent Bundle of the Hypersurfaces in a Euclidean Space

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...