A basic decomposition result related to the notion of the rank of a matrix and applications.
A matrix-polynomial structure in a finite-dimensional vector space.
A new decomposition for square matrices.
A new family of companion forms of polynomial matrices.
A note on the cp-rank of matrices generated by Soules matrices.
A propos de l’algorithme
A simple cocyclic Jacket matrices.
A simple proof of polar decomposition in pseudo-Euclidean geometry
We give a simple direct proof of the polar decomposition for separated linear maps in pseudo-Euclidean geometry.
A study on new right/left inverses of nonsquare polynomial matrices
This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called τ-inverses, σ-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The applicationoriented problem of selecting stable inverses is also solved. Applications in inverse-model control, in particular robust minimum...
A transvection decomposition in GL(n,2)
An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.
Algebraic theory of fast mixed-radix transforms. I. Generalized Kronecker product of matrices
Algebraic theory of fast mixed-radix transforms. II. Computational complexity and applications
Algorithm of -factorization of rational matrices with zeros and poles on the imaginary axis.
Alternating projected Barzilai-Borwein methods for nonnegative matrix factorization.
An Alternative Givens Ordering.
An analysis of GCD and LCM matrices via the -factorization.
An approach based on matrix polynomials for linear systems of partial differential equations
In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals that the method...
An Efficient Method for Calculating Smoothing Splines Using Orthogonal Transformations.
An explicit factorization of totally positive generalized Vandermonde matrices avoiding Schur functions.
An improved characterisation of the interior of the completely positive cone.