An inequality for non-negative matrices

✍ Scribed by Ming-wei Wang; Jeffrey Shallit

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 391 KB
• Volume: 290
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(98)10207-0

✦ Synopsis

Let A be an n x n matrix with non-negative entries and no entry in (0, 1). We prove that there exist integers r, s with 0 <~ r < s ~< 2" such that A" <~ AL We prove that 2" cannot be replaced with e~.

We also give an application to the theory of formal languages.