On the -th roots of a complex matrix.
On the orbit of the centralizer of a matrix
Let A be a complex n × n matrix. Let A' be its commutant in Mₙ(ℂ), and C(A) be its centralizer in GL(n,ℂ). Consider the standard C(A)-action on ℂⁿ. We describe the C(A)-orbits via invariant subspaces of A'. For example, we count the number of C(A)-orbits as well as that of invariant subspaces of A'.
On the principal minors of a matrix with a multiple eigenvalue.
On the Rodman-Shalom conjecture regarding the Jordan form of completions of partial upper triangular matrices.
On the singular decomposition of matrices.
On the singular graph and the Weyr characteristic of an M-matrix.
On the Solution of sigma-alpha Regular Generalized Linear Systems
On the span invariant for cubic similarity
Given a real n×n matrix A, we make some conjectures and prove partial results about the range of the function that maps the n-tuple x into the entrywise kth power of the n-tuple Ax. This is of interest in the study of the Jacobian Conjecture.
On the structure of nilpotent endomorphisms and applications.
On the Yang-Baxter-like matrix equation for rank-two matrices
Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.
On uniform symmetrization of analytic matrix functions
Orthogonal diagonalization for complex skew-persymmetric anti-tridiagonal Hankel matrices
In this paper, we obtain an eigenvalue decomposition for any complex skew-persymmetric anti-tridiagonal Hankel matrix where the eigenvector matrix is orthogonal.
Pairs of matrices, one of which commutes with their commutator.
Patterns of commutativity: the commutant of the full pattern.
Pencils of real symmetric matrices and the numerical range.
Periodic coprime matrix fraction decompositions.
Perturbations of functions of diagonalizable matrices.
Polynomial sequences generated by infinite Hessenberg matrices
We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz...
Primary decomposition of torsion -modules.
Pseudo-similarity and partial unit regularity