New bounds for the greatest characteristic root of a nonnegative matrix are obtained. They generalize and improve the bounds of G. Frobenius and H. Mint. 1. INTRODUCTION Let .4 = (u,~> be a nonnegative matrix of order n, and rr, r2,. . . , rn its row sums. The following results of Frobenius [I] are
On the greatest distance between two permanental roots of a matrix
✍ Scribed by Arnold R Kräuter
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 863 KB
- Volume
- 93
- Category
- Article
- ISSN
- 0024-3795
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📜 SIMILAR VOLUMES
We prove diophantine inequalities involving various distances between two distinct algebraic points of an algebraic curve. These estimates may be viewed as extensions of classical Liouville's inequality. Our approach is based on a transcendental construction using algebraic functions. Next we apply
## Abstract In this note, we show how the determinant of the distance matrix __D(G__) of a weighted, directed graph __G__ can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks __G~i~__ of __G__. In particular, when cof __D(G__), the sum of the cofactors of _
Davison and Ramesh expressed equivalently the condition for the characteristic roots of a real matrix to lie within a sector by the condition