All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 77 Next

Displaying 1521 – 1540 of 3024

Showing per page

Norm estimates for solutions of matrix equations AX-XB=C and X-AXB=C

Michael I. Gil' (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let A, B and C be matrices. We consider the matrix equations Y-AYB=C and AX-XB=C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.

Note on a conjecture for the sum of signless Laplacian eigenvalues

Xiaodan Chen, Guoliang Hao, Dequan Jin, Jingjian Li (2018)

Czechoslovak Mathematical Journal

For a simple graph G on n vertices and an integer k with 1 ≤ k ≤ n , denote by 𝒮 k + ( G ) the sum of k largest signless Laplacian eigenvalues of G . It was conjectured that 𝒮 k + ( G ) ≤ e ( G ) + k + 1 2 , where e ( G ) is the number of edges of G . This conjecture has been proved to be true for all graphs when k ∈ { 1 , 2 , n - 1 , n } , and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all k ). In this note, this conjecture is proved to be true for all graphs when k = n - 2 , and for some new classes of graphs.

Note on some greatest common divisor matrices

Peter Lindqvist, Kristian Seip (1998)

Acta Arithmetica

Some quadratic forms related to "greatest common divisor matrices" are represented in terms of L²-norms of rather simple functions. Our formula is especially useful when the size of the matrix grows, and we will study the asymptotic behaviour of the smallest and largest eigenvalues. Indeed, a sharp bound in terms of the zeta function is obtained. Our leading example is a hybrid between Hilbert's matrix and Smith's matrix.

Note on strongly nil clean elements in rings

Aleksandra Kostić, Zoran Z. Petrović, Zoran S. Pucanović, Maja Roslavcev (2019)

Czechoslovak Mathematical Journal

Let R be an associative unital ring and let a ∈ R be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.

Note on the ANOVA of a completely confounded factorial experiment

Wiktor Oktaba (2005)

Applicationes Mathematicae

The purpose of this paper is to present a modern approach to the analysis of variance (ANOVA) of disconnected resolvable group divisible partially balanced incomplete block (GDPBIB) designs with factorial structure and with some interaction effects completely confounded. A characterization of a factorial experiment with completely confounded interaction is given. The treatment effect estimators and some relations between the matrix F of the reduced normal equations and the information matrix A are...

Currently displaying 1521 – 1540 of 3024