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 Hadamard product and related dilations
The Hankel transform and some of its properties.
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.
The Hurwitz Matrix Equations and Multifour Groups.
The importance of each node in a structure of links: Google-PageRank.
The Indecomposable Representations of the Dihedral 2-Groups.
The inertia of Hermitian tridiagonal block matrices.
The inertia set of nonnegative symmetric sign pattern with zero diagonal
The inertia set of a symmetric sign pattern is the set , where denotes the inertia of real symmetric matrix , and denotes the sign pattern class of . In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns with zero diagonal that require...
The interplay between classical analysis and (numerical) linear algebra -- a tribute to Gene H. Golub.
The inverse eigenvalue and inertia problems for minimum rank two graphs.
The inverse of the Pascal lower triangular matrix modulo .
The Jordan forms of and .
The k-Fibonacci matrix and the Pascal matrix
We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.
The Laplacian permanental polynomial for trees