Constructing copositive matrices from interior matrices.
Controllability, Bezoutian and relative primeness.
Criteria of unitary equivalence of Hermitian operators with a degenerate spectrum.
Cylinder matrices
Determinant and inverse of meet and join matrices.
Determinants of matrices associated with incidence functions on posets
Let be a finite subset of a partially ordered set . Let be an incidence function of . Let denote the matrix having evaluated at the meet of and as its -entry and denote the matrix having evaluated at the join of and as its -entry. The set is said to be meet-closed if for all . In this paper we get explicit combinatorial formulas for the determinants of matrices and on any meet-closed set . We also obtain necessary and sufficient conditions for the matrices...
Diagonal blocks of two mutually inverse positive definite block matrices
Drei-Nachrichten-Probleme in verallgemeinerter Definition.
Eigenvalue distribution of certain ray patterns
In this paper, the eigenvalue distribution of complex matrices with certain ray patterns is investigated. Cyclically real ray patterns and ray patterns that are signature similar to real sign patterns are characterized, and their eigenvalue distribution is discussed. Among other results, the following classes of ray patterns are characterized: ray patterns that require eigenvalues along a fixed line in the complex plane, ray patterns that require eigenvalues symmetric about a fixed line, and ray...
Eigenvalues and eigenvectors of some tridiagonal matrices with non-constant diagonal entries
We give explicit expressions for the eigenvalues and eigenvectors of some tridiagonal matrices with non-constant diagonal entries. Our techniques are based on the theory of recurrent sequences.
Eigenvalues and eigenvectors of tridiagonal matrices.
Eigenvalues of several tridiagonal matrices.
Eigenvalues of sums of pseudo-Hermitian matrices.
Eigenvector Matrices of Symmetric Tridiagonals.
Eigenvectors of acyclic matrices
Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices
We use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict k-Hessenberg matrices and banded matrices. Our results can be extended to the cases of block triangular and block Hessenberg matrices. An n × n lower triangular matrix is called elementary if it is of the form I + C, where I is the identity matrix and C is lower triangular and has all of its nonzero entries...
Equalities for orthogonal projectors and their operations
A complex square matrix A is called an orthogonal projector if A 2 = A = A*, where A* denotes the conjugate transpose of A. In this paper, we give a comprehensive investigation to matrix expressions consisting of orthogonal projectors and their properties through ranks of matrices. We first collect some well-known rank formulas for orthogonal projectors and their operations, and then establish various new rank formulas for matrix expressions composed by orthogonal projectors. As applications, we...
Equivalence and congruence of matrices under the action of standard parabolic subgroups.
Essential decomposition of polynomially normal matrices in real indefinite inner product spaces.
Essentially Hermitian matrices revisited.