The eigenvalue distribution of block diagonally dominant matrices and block H-matrices.
The eigenvalue distribution on Schur complement of nonstrictly diagonally dominant matrices and general -matrices.
The Eigenvalues and Singular Values of Matrix Sums and Product, VIII: Displacement of Indices
The eigenvalues of Hermite and rational spectral differentiation matrices.
The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices
In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.
The equation and the dimension of *congruence orbits.
The equations of conjugacy classes of nilpotent matrices.
The explicit representations of the Drazin inverses of a class of block matrices.
The external vertices conjecture in case .
The extremal ranks of subject to a pair of matrix equations
The fan graph is determined by its signless Laplacian spectrum
Given a graph , if there is no nonisomorphic graph such that and have the same signless Laplacian spectra, then we say that is -DS. In this paper we show that every fan graph is -DS, where and .
The fundamental cone and the Minkowski cone.
The general Hermitian nonnegative-definite solution to the matrix equation .
The general linear equation on vector spaces.
The general totally positive matrix completion problem with few unspecified entries.
The generalized Radon-Hurwitz numbers
The Gerschgorin discs under unitary similarity
The intersection of the Gerschgorin regions over the unitary similarity orbit of a given matrix is studied. It reduces to the spectrum in some cases: for instance, if the matrix satisfies a quadratic equation, and also for matrices having "large" singular values or diagonal entries. This leads to a number of open questions.
The group of commutativity preserving maps on strictly upper triangular matrices
Let be the algebra of all strictly upper triangular matrices over a unital commutative ring . A map on is called preserving commutativity in both directions if . In this paper, we prove that each invertible linear map on preserving commutativity in both directions is exactly a quasi-automorphism of , and a quasi-automorphism of can be decomposed into the product of several standard maps, which extains the main result of Y. Cao, Z. Chen and C. Huang (2002) from fields to rings.
The higher rank numerical range of nonnegative matrices
In this article the rank-k numerical range ∧k (A) of an entrywise nonnegative matrix A is investigated. Extending the notion of elements of maximum modulus in ∧k (A), we examine their location on the complex plane. Further, an application of this theory to ∧k (L(λ)) of a Perron polynomial L(λ) is elaborated via its companion matrix C L.