In this paper we present a new diagonal balancing technique for regular matrix pencils λB − A, which aims at reducing the sensitivity of the corresponding generalized eigenvalues. It is inspired from the balancing technique of a square matrix A and has a comparable complexity. Upon convergence, the diagonally scaled pencil has row and column norms that are balanced in a precise sense. We also s...

The objective of this paper is to study the theoretical analysis of linear differential-algebraic equations (DAEs) of higher order as well as the regularity and singularity of matrix polynomials. Some invariants and condensed forms under appropriate equivalent transformations are established for systems of linear higher-order DAEs with constant and variable coefficients. Inductively, based on c...

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.