EuDML | Browse

In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.

The equation $X A + A X^{} = 0$ and the dimension of congruence orbits.

De Terán, Fernando, Dopico, Froilán M. (2011)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The equations of conjugacy classes of nilpotent matrices.

J. Weyman (1989)

Inventiones mathematicae

The explicit representations of the Drazin inverses of a class of block matrices.

Bu, Changjiang, Zhang, Kuize (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The external vertices conjecture in case $n = 4$ .

Drury, S.W. (2004)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The extremal ranks of $A_{1} - B_{1} X C_{1}$ subject to a pair of matrix equations

Yongge Tian, Yonghui Liu (2006)

Rendiconti del Seminario Matematico della Università di Padova

The fan graph is determined by its signless Laplacian spectrum

Muhuo Liu, Yuan Yuan, Kinkar Chandra Das (2020)

Czechoslovak Mathematical Journal

Given a graph $G$ , if there is no nonisomorphic graph $H$ such that $G$ and $H$ have the same signless Laplacian spectra, then we say that $G$ is $Q$ -DS. In this paper we show that every fan graph $F_{n}$ is $Q$ -DS, where $F_{n} = K_{1} \lor P_{n - 1}$ and $n \geq 3$ .

The fundamental cone and the Minkowski cone.

A.J. Crisalli (1975)

Journal für die reine und angewandte Mathematik

The general Hermitian nonnegative-definite solution to the matrix equation $A X A^{} + B Y B^{} = C$ .

Zhang, Xian (2005)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

The general linear equation on vector spaces.

Kečkić, Jovan D. (1985)

Publications de l'Institut Mathématique. Nouvelle Série

The general totally positive matrix completion problem with few unspecified entries.

Fallat, Shaun M., Johnson, Charles R., Smith, Ronald L. (2000)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The generalized Radon-Hurwitz numbers

Marc A. Berger, Shmuel Friedland (1986)

Compositio Mathematica

The Gerschgorin discs under unitary similarity

Anna Zalewska-Mitura, Jaroslav Zemánek (1997)

Banach Center Publications

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

Deng Yin Wang, Min Zhu, Jianling Rou (2014)

Czechoslovak Mathematical Journal

Let $𝒩 = N_{n} (R)$ be the algebra of all $n \times n$ strictly upper triangular matrices over a unital commutative ring $R$ . A map $ϕ$ on $𝒩$ is called preserving commutativity in both directions if $x y = y x \Leftrightarrow ϕ (x) ϕ (y) = ϕ (y) ϕ (x)$ . In this paper, we prove that each invertible linear map on $𝒩$ preserving commutativity in both directions is exactly a quasi-automorphism of $𝒩$ , and a quasi-automorphism of $𝒩$ 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

Aikaterini Aretaki, Ioannis Maroulas (2013)

Open Mathematics

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.

Currently displaying 41 – 60 of 194

Previous Page 3 Next