We survey some unusual eigenvalue problems arising in different applications. We show that all these problems can be cast as problems of estimating quadratic forms. Numerical algorithms based on the well-known Gauss-type quadrature rules and Lanczos process are reviewed for computing these quadratic forms. These algorithms reference the matrix in question only through a matrix-vector product op...

The matrix forms for curves and surfaces were largely promoted in CAD/CAM. In this paper we have presented two matrix representation formulations for arbitrary degree NURBS curves and surfaces explicitly other than recursively. The two approaches are derived from the computation of divided difference and the Marsden identity respectively. The explicit coefficient matrix of B-spline with equally...

In this paper a new family of companion forms associated to a regular polynomial matrix is presented. Similar results have been presented in a recent paper by M. Fiedler, where the scalar case is considered. It is shown that the new family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen a...

This paper presents results from a production experiment in Hindi, showing that differences in attachment site of object relative clauses result in prosodic differences when the antecedent of the relative clause (RC) is part of a complex NP with the structure N1 of N2. In particular, based on duration and F0 data we argue that the phrasing in a matrix sentence encodes the attachment site of the...

In this paper we unify the two subjects of implicitization and parametrization of nonsingular cubic surfaces. Beginning with a cubic parametrization with six basepoints, we first form a three by four Hilbert–Burch matrix, and then a three by three matrix of linear forms whose determinant is the implicit equation. Beginning with an implicit equation, we show how to construct a three by three mat...

Abstract We consider the possible Jordan canonical forms of Riordan arrays. prove that there are, in fact, only two such forms. Moreover, transition matrix is group case when given array has one some three specific

in the present paper, we introduce the sequence space [{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},] where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. we investigate its topological properties and inclusion relations. moreover, we consider the problem of fin...

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 . . . . . . . . . . . . . . . . . . ....