We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...

5 Applications of Linear Algebra 24 5.1 The Cayley-Hamilton Theorem . . . . . . . . . . . . . . . . . . . 24 5.2 Solving State Equations . . . . . . . . . . . . . . . . . . . . . . . 24 5.3 Matrix Decompositions . . . . . . . . . . . . . . . . . . . . . . . 29 5.4 Bilinear Forms and Sign-definite Matrices . . . . . . . . . . . . . 32 5.4.1 Definite Matrices . . . . . . . . . . . . . . . . . . ....

SUMMARY StratiGraph, a Java-based tool for computation and presentation of closure hierarchies of Jordan and Kronecker structures is presented. The tool is based on recent theoretical results on stratiications of orbits and bundles of matrices and matrix pencils. A stratiication reveals the complete hierarchy of nearby structures, information critical for explaining the qualitative behavior of ...

Before we can show how to apply the ring theory that we have developed to linear transformations of vector spaces we need to set up some results on polynomial factorizaton. Let F be a field and let x be an indeterminate. Set R = F [x]. Then as we have seen R is a P.I.D. so in particular a unique factorization domain. Noting that if f(x), g(x) ∈ F [x] then deg(f(x)g(x)) = deg(f(x)) + deg(g(x)) w...

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In this article, we propose a method to perform linear algebra on a matrix with nearly sparse properties. More precisely, although we require the main part of the matrix to be sparse, we allow some dense columns with possibly large coefficients. We modify Block Wiedemann algorithm and show that the contribution of these heavy columns can be made negligible compared to the one of the sparse part...

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