Abstract. By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli-type matrices for a given skew Schur function are stably equivalent to each other over symmetric functions. As a consequence, the Jacobi-Trudi matrix and the transpose of the dual Jacobi-Trudi matrix are stably equivalent over symmetric functions. This leads to an affirm...

Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)dimensional case, the corresponding system can be extended to 2 × 2 matrix form. The factorization theorem of the Christoffel kernel for s...

A new implicitly-restarted Krylov subspace method for real symmetric/skew-symme– tric generalized eigenvalue problems is presented. The new method improves and generalizes the SHIRA method of [37] to the case where the skew symmetric matrix is singular. It computes a few eigenvalues and eigenvectors of the matrix pencil close to a given target point. Several applications from control theory are...

Structure-preserving numerical techniques for computation of eigenvalues and stable deflating subspaces of complex skew-Hamiltonian/Hamiltonian matrix pencils, with applications in control systems analysis and design, are presented. The techniques use specialized algorithms to exploit the structure of such matrix pencils: the skew-Hamiltonian/Hamiltonian Schur form decomposition and the periodi...

The sensitivity of a multiple eigenvalue of a matrix under perturbations can be measured by its Hölder condition number. Various extensions of this concept are considered. A meaningful notion of structured Hölder condition numbers is introduced and it is shown that many existing results on structured condition numbers for simple eigenvalues carry over to multiple eigenvalues. The structures inv...

In this paper, we present some new lower and upper bounds for the modified Randic index in terms of maximum, minimum degree, girth, algebraic connectivity, diameter and average distance. Also we obtained relations between this index with Harmonic and Atom-bond connectivity indices. Finally, as an application we computed this index for some classes of nano-structures and linear chains.

By using the (generalized) Goethals-Seidel array, we construct Hadamard matrices of skew type of order 4n for n = 81,103,151,169, and 463. Hadamard matrices of skew type for these orders are constructed here for the first time. Consequently the list of odd integers n < 300 for which no Hadamard matrix of skew type of order 4n is presently known is reduced to 45 numbers (see the comments after t...

The covariance matrix of a pattern is composed by its second order central moments. For a rotationally symmetric shape, its covariance matrix is a scalar identity matrix. In this work, we apply this property to restore the skewed shape of rotational symmetry. The relations between the skew transformation matrix and the covariance matrices of original and skewed shapes are derived. By computing ...

We develop a computer code that uses elegant bit-manipulation techniques for matrix multiplication and thus facilitates exhaustive generation of Skew-Hadamard matrices. Hadamard matrices are useful in spectroscopic applications (Hadamard transform spectroscopy) and in balanced chemical designs. Application of our code yields several Skew-Hadamard matrices up to order 100 X 100, although the com...