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Displaying 1 – 20 of 41

On a bound on algebraic connectivity: the case of equality

Stephen J. Kirkland, Neumann, Michael, Bryan L. Shader (1998)

Czechoslovak Mathematical Journal

In a recent paper the authors proposed a lower bound on $1 - λ_{i}$ , where $λ_{i}$ , $λ_{i} \neq 1$ , is an eigenvalue of a transition matrix $T$ of an ergodic Markov chain. The bound, which involved the group inverse of $I - T$ , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...

On a group of mixed-type reverse-order laws for generalized inverses of a triple matrix product with applications.

Tian, Yongge, Liu, Yonghui (2007)

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

On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems.

Fritzsche, Bernd, Kirstein, Bernd, Sakhnovich, Alexander L. (2008)

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

On a Schur complement inequality for the Hadamard product of certain totally nonnegative matrices.

Yang, Zhongpeng, Feng, Xiaoxia (2011)

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

On a System of Functional Equations

Jovan D. Kečkić (1988)

Publications de l'Institut Mathématique

On block triangular matrices with signed Drazin inverse

Changjiang Bu, Wenzhe Wang, Jiang Zhou, Lizhu Sun (2014)

Czechoslovak Mathematical Journal

The sign pattern of a real matrix $A$ , denoted by $sgn A$ , is the $(+, -, 0)$ -matrix obtained from $A$ by replacing each entry by its sign. Let $𝒬 (A)$ denote the set of all real matrices $B$ such that $sgn B = sgn A$ . For a square real matrix $A$ , the Drazin inverse of $A$ is the unique real matrix $X$ such that $A^{k + 1} X = A^{k}$ , $X A X = X$ and $A X = X A$ , where $k$ is the Drazin index of $A$ . We say that $A$ has signed Drazin inverse if $sgn {\tilde{A}}^{d} = sgn A^{d}$ for any $\tilde{A} \in 𝒬 (A)$ , where $A^{d}$ denotes the Drazin inverse of $A$ . In this paper, we give necessary conditions for some block triangular matrices to have signed...

On commuting generalized inverses in semigroups.

Kečkić, Jovan D., Milić, Svetozar (1999)

Publications de l'Institut Mathématique. Nouvelle Série

On commuting generalized inverses of matrices and in associative rings.

Kečkić, Jovan D. (2001)

Publications de l'Institut Mathématique. Nouvelle Série

On Davis-Kahan-weinberger Extension Theorem

Dragan S. Đorđević (2002)

Matematički Vesnik

On generalized inverses of banded matrices.

Bapat, R.B. (2007)

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

On inverses of triangular matrices with monotone entries.

Berenhaut, Kenneth S., Fletcher, Preston T. (2005)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On Inverses of Vandermonde and Confluent Vandermonde Matrices III.

W. Gautschi (1977/1978)

Numerische Mathematik

On linear operators strongly preserving invariants of Boolean matrices

Yizhi Chen, Xian Zhong Zhao (2012)

Czechoslovak Mathematical Journal

Let $𝔹_{k}$ be the general Boolean algebra and $T$ a linear operator on $M_{m, n} (𝔹_{k})$ . If for any $A$ in $M_{m, n} (𝔹_{k})$ ( $M_{n} (𝔹_{k})$ , respectively), $A$ is regular (invertible, respectively) if and only if $T (A)$ is regular (invertible, respectively), then $T$ is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over $𝔹_{k}$ . Meanwhile, noting that a general Boolean algebra $𝔹_{k}$ is isomorphic...

On matrices with all minors negative.

Fallat, Shaun M., van den Driessche, P. (2000)

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

On matrix convexity of the Moore-Penrose inverse.

Mond, B., Pečarić, J.E. (1996)

International Journal of Mathematics and Mathematical Sciences

On melancholic magic squares

Götz Trenkler, Dietrich Trenkler (2013)

Discussiones Mathematicae Probability and Statistics

Starting with Dürer's magic square which appears in the well-known copper plate engraving Melencolia we consider the class of melancholic magic squares. Each member of this class exhibits the same 86 patterns of Dürer's magic square and is magic again. Special attention is paid to the eigenstructure of melancholic magic squares, their group inverse and their Moore-Penrose inverse. It is seen how the patterns of the original Dürer square to a large extent are passed down also to the inverses of the...

On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product.

Tian, Yongge (2004)

International Journal of Mathematics and Mathematical Sciences

On Moore-Penrose Inverse of Block Matrices and Full-rank Factorization

Gradimir V. Milovanović, Predrag Stanimirović (1997)

Publications de l'Institut Mathématique

On orderings induced by the Loewner partial ordering

Jan Hauke, Augustyn Markiewicz (1994)

Applicationes Mathematicae

The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.

On polynomial $E P_{r}$ matrices.

Meenakshi, Ar., Anandam, N. (1992)

International Journal of Mathematics and Mathematical Sciences

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