Bounds for the right spectral radius of quaternionicmatrices

Sharp Bounds on the PI Spectral Radius

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

sharp bounds on the pi spectral radius

in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

Bounds for the Spectral Radius of a Matrix

Let A = [an] be an n X n matrix with complex entries. We define p(A ) to be the spectral radius of A and | A | to be the matrix [| a,y |]. A. Brauer [1], W. Ledermann [2] and A. Ostrowski [4] have developed bounds for p(\ A |). Their results, coupled with the result of Perron and Frobenius [6] that p(A) ^ p(\ A |) give upper bounds for p( A ) which are not less than p(\ A | ). These bounds are ...

Bounds for the Laplacian spectral radius of graphs

Lower bounds for the spectral radius of a matrix

In this paper we develop lower bounds for the spectral radius of symmetric , skew{symmetric, and arbitrary real matrices. Our approach utilizes the well{known Leverrier{Faddeev algorithm for calculating the co-eecients of the characteristic polynomial of a matrix in conjunction with a theorem by Lucas which states that the critical points of a polynomial lie within the convex hull of its roots....