NEW UPPER BOUNDS ON THE SPECTRAL RADIUS OF THE HADAMARD PRODUCT OF NONNEGATIVE MATRICES

2020 ◽  
Vol 48 (2) ◽  
pp. 121-131
Author(s):  
Leena Sharma ◽  
V. H. Badshah ◽  
H. K. Patel
Keyword(s):  
Spectral Radius ◽  
Hadamard Product ◽  
Upper Bounds ◽  
Nonnegative Matrices

scholarly journals Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 147
Author(s):  
Qianping Guo ◽  
Jinsong Leng ◽  
Houbiao Li ◽  
Carlo Cattani
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Upper Bound ◽  
Hadamard Product ◽  
Simple Type ◽  
Nonnegative Matrices ◽  
Minimum Eigenvalue ◽  
Numerical Examples ◽  
Product Of Matrices

In this paper, an upper bound on the spectral radius ρ ( A ∘ B ) for the Hadamard product of two nonnegative matrices (A and B) and the minimum eigenvalue τ ( C ★ D ) of the Fan product of two M-matrices (C and D) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several M-matrices is also presented. These results and numerical examples show that the new bounds improve some existing results.

scholarly journals Norm of nonnegative and positive matrices

2017 ◽  
Vol 6 (3) ◽  
pp. 98
Author(s):  
Alaa Abu Alroz
Keyword(s):  
Spectral Radius ◽  
Lower Bounds ◽  
Maximum Modulus ◽  
Upper Bounds ◽  
Nonnegative Matrices ◽  
Lower And Upper Bounds ◽  
Positive Matrix ◽  
Eigen Value ◽  
Eigen Values ◽  
Positive Matrices

The spectral radius r(A) of matrix A is the maximum modulus of the Eigen values. In this paper, the studies about the lower and upper bounds for the spectral radius and the lower bounds for the minimum eigen value of appositive and nonnegative matrices are investigate.The matrix norm, the spectral radius norm,and the column (row) sums of nonnegative and positive matrices are widely used to establish some inequalities for matrices. Then several existing results are improved for these inequalities for nonnegative and positive matrix. Furthermore, the lower and upper bounds of the Perron roots for nonnegative matrices are examined, and some upper bounds are computed.

scholarly journals Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices

2018 ◽  
Author(s):  
Qianping Guo ◽  
Jinsong Leng ◽  
Houbiao Li ◽  
Carlo Cattani
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Mixed Type ◽  
Hadamard Product ◽  
Simple Type ◽  
Nonnegative Matrices ◽  
Minimum Eigenvalue ◽  
Numerical Examples ◽  
Special Cases ◽  
Product Of Matrices

In this paper, some mixed type bounds on the spectral radius $\rho(A\circ B)$ for the Hadamard product of two nonnegative matrices ($A$ and $B$) and the minimum eigenvalue $\tau(C\star D)$ of the Fan product of two $M$-matrices ($C$ and $D$) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several $M$-matrices is also presented: $$ \tau(A_{1}\star A_{2}\cdots\star A_{m})\geq \min_{1\leq i\leq n}\{\prod^{m}_{k=1}A_{k}(i,i)-\prod^{m}_{k=1}[A_{k}(i,i)^{P_{k}}-\tau(A_{k}^{(P_{k})})]^\frac{1}{P_{k}}\}, $$ where $A_{1},\ldots, A_{k}$ are $n\times n$ $M$-matrices and $P_{1},\ldots, P_{k}>0$ satisfy $\sum^{m}_{k=1}\frac{1}{P_{k}}\geq 1$. Some special cases of the above result and numerical examples show that this new bound improves some existing results.

scholarly journals Maximizing the spectral radius of fixed trace diagonal perturbations of nonnegative matrices

1996 ◽  
Vol 241-243 ◽  
pp. 635-654 ◽  
Author(s):  
Charles R. Johnson ◽  
Raphael Loewy ◽  
D.D. Olesky ◽  
P. van den Driessche
Keyword(s):  
Spectral Radius ◽  
Nonnegative Matrices

scholarly journals Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yajing Wang ◽  
Yubin Gao
Keyword(s):  
Graph Theory ◽  
Spectral Radius ◽  
Adjacency Matrix ◽  
Upper Bounds ◽  
Simple Graph ◽  
Spectral Graph Theory ◽  
Extremal Graphs ◽  
Spectral Graph ◽  
Vertex Set

Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

Sign in / Sign up

Export Citation Format

Share Document