1. Some properties complementary to Brualdi-Li matrices
- Creator:
- Wang, Chuanlong and Yong, Xuerong
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- tournament matrix, Brualdi-Li matrix, eigenvalue, and Perron value
- Language:
- English
- Description:
- In this paper we derive new properties complementary to an $2n \times 2n$ Brualdi-Li tournament matrix $B_{2n}$. We show that $B_{2n}$ has exactly one positive real eigenvalue and one negative real eigenvalue and, as a by-product, reprove that every Brualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of $B_{2n}$ is also determined. Related results obtained in previous articles are proven to be corollaries.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public