Explicit polar decomposition of companion matrices.
Explicit polar decomposition of complex matrices.
Factorizable matrices
We study square matrices which are products of simpler factors with the property that any ordering of the factors yields a matrix cospectral with the given matrix. The results generalize those obtained previously by the authors.
Factorization Iterative Methods, M-Operators and H-Operators.
Factorizations of matrices and functions of two variables
Fast Toeplitz Orthogonalization.
Full rank factorization and the Flanders theorem.
Gegenbauer polynomials and semiseparable matrices.
Generalized Pascal -eliminated functional matrix with variables.
Generalized Pascal triangles and Toeplitz matrices.
Generating functions via Hankel and Stieltjes matrices.
G-matrices, -orthogonal matrices, and their sign patterns
A real matrix is a G-matrix if is nonsingular and there exist nonsingular diagonal matrices and such that , where denotes the transpose of the inverse of . Denote by a diagonal (signature) matrix, each of whose diagonal entries is or . A nonsingular real matrix is called -orthogonal if . Many connections are established between these matrices. In particular, a matrix is a G-matrix if and only if is diagonally (with positive diagonals) equivalent to a column permutation of...
Hankel-matrix approach to invertibility of linear multivariable systems
(Homogeneous) markovian bridges
(Homogeneous) Markov bridges are (time homogeneous) Markov chains which begin at a given point and end at a given point. The price to pay for preserving the homogeneity is to work with processes with a random life-span. Bridges are studied both for themselves and for their use in describing the transformations of Markov chains: restriction on a random interval, time reversal, time change, various conditionings comprising the confinement in some part of the state space. These bridges lead us to look...
How to establish universal block-matrix factorizations.
Hybrid Algorithm for Fast Toeplitz Orthogonalization.
Implementing an interior point method for linear programs on a CPU-GPU system.
Incomplete matrix partial fraction expansion
Interior points of the completely positive cone.
Involutions and semiinvolutions
We define a linear map called a semiinvolution as a generalization of an involution, and show that any nilpotent linear endomorphism is a product of an involution and a semiinvolution. We also give a new proof for Djocović’s theorem on a product of two involutions.