Geodesic
Some properties complementary to Brualdi-Li matrices
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 135-149 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10587-015-0164-7
Classification : 05C20, 05C50, 15A15
Keywords: tournament matrix; Brualdi-Li matrix; eigenvalue; Perron value 
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Wang, Chuanlong; Yong, Xuerong. Some properties complementary to Brualdi-Li matrices. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 135-149. doi: 10.1007/s10587-015-0164-7

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