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Details for article 12 of 12 found articles
| Title: |
Tournament matrices and their generalizations, I. |
| Author: |
Maybee, John S. Pullman, Norman J. |
| Appeared in: |
Linear & multilinear algebra |
| Paging: | Volume 28 (1990) nr. 1-2 pages 57-70 |
| Year: |
1990-10 |
| Contents: |
If M is any complex matrix with rank (M + M* + I) = 1, we show that any eigenvalue of M that is not geometrically simple has 1/2 for its real part. This generalizes a recent finding of de Caen and Hoffman: the rank of any n × n tournament matrix is at least n - 1. We extend several spectral properties of tournament matrices to this and related types of matrices. For example, we characterize the singular real matrices M with 0 diagonal for which rank (M + MT + I) = 1 and we characterize the vectors that can be in the kernels of such matrices. We show that singular, irreducible n × n tournament matrices exist if and only n∉ {2,3,4,5} and exhibit many infinite families of such matrices. Connections with signed digraphs are explored and several open problems are presented. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 12 of 12 found articles
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