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In this paper we derive new properties complementary to an $2 n \times 2 n$ Brualdi-Li tournament matrix $B_{2 n}$ . We show that $B_{2 n}$ 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 $B_{2 n}$ is also determined. Related results obtained in previous articles are proven to be corollaries.

Some properties of the $q$ -adic Vandermonde matrix.

Mani, Vaidyanath, Hartwig, Robert E. (1996)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Some remarks on the solutions of the equality per $(z I - A) = 0$ . (Einige Bemerkungen über die Lösungen der Gleichung per $(z I - A) = 0$ .)

Kräuter, Arnold Richard (1987)

Séminaire Lotharingien de Combinatoire [electronic only]

Some variations on the concept of the c-numerical range

Bebiano, Natália (1985/1986)

Portugaliae mathematica

SomeRremarks on a Combinatorial Problem

Josef Kaucký (1972)

Matematický časopis

Spectral properties of a certain class of Carleman operators

S. M. Bahri (2007)

Archivum Mathematicum

The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space $L^{2} (X, μ)$ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of $A$ and then using the Stieltjes inversion formula.

Sulle forme polarizzanti i coefficienti del polinomio caratteristico di una matrice

Renzo Mazzocco (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The multilinear forms, obtained by polarizing the coefficients of the characteristic polynomial of a matrix, are considered. A general relation (formula A) between such forms is proved. It follows in particular a rational expression for the above-mentioned coefficients (formula C), which is in a sense analogous to Newton's formulas, but with the use of the determinant function instead of the trace function.

Sur la calculabilité des déterminants de matrices d'opérateurs différentiels

Kossivi Adjamagbo (1985)

Publications mathématiques et informatique de Rennes

Sur la résultante de trois formes quadratiques ternaires

R. Radau (1869)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

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