Abstract
We determine the maximum and minimum numbers of positive entries of imprimitive nonnegative matrices with a given imprimitivity index. One application of the results is to estimate the imprimitivity index by the number of positive entries. The proofs involve the study of a cyclic quadratic form. This completes a research initiated by Lewin in 1990.
| Original language | English |
|---|---|
| Pages (from-to) | 132-138 |
| Number of pages | 7 |
| Journal | Linear Algebra and Its Applications |
| Volume | 424 |
| Issue number | 1 SPEC. ISS. |
| DOIs | |
| State | Published - 1 Jul 2007 |
Keywords
- Imprimitive matrix
- Nonnegative matrix
- Quadratic form