Bounds for the greatest characteristic root of a nonnegative matrix

✍ Scribed by Shu-Lin Liu

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 446 KB
• Volume: 239
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(96)90008-7

✦ Synopsis

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 well known. The greatest characteristic root r, sometimes called Perron root, satisfies minri < r < maxr,, i I r 3 maxnii.

i A result similar to (1.1) holds for column sums c,, c,, . . . , c,.