Maximization of quadratic forms expressed by distance matrices
IZUMINO, Saichi ; NAKAMURA, Noboru
Hokkaido Math. J., Tome 35 (2006) no. 1, p. 641-658 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
If $x,y,z$ are real numbers satisfying $x+y+z=1$, then the maximum of the quadratic form $axy+bxz+cyz$ with positive constants $a,b,c$ is $$\displaystyle{\frac{abc}{2ab+2ac+2bc-a^2-b^2-c^2}}$$ under the assumption $\sqrt{a}<\sqrt{b}+\sqrt{c}$. Extending this fact, we give the maximum of the quadratic form $\displaystyle\sum_{1 \le i< j \le n} a_{ij}x_i x_j$ in $n$-variables $x_1,\ldots,x_n$ satisfying $\displaystyle\sum_{i=1}^{n} x_i = 1$ with constants $a_{ij} \ge 0$ under certain assumptions.
Publié le : 2006-08-15
Classification:  distance matrix,  quadratic form,  Ozeki's inequality,  15A63,  15A48 
@article{1285766422,
     author = {IZUMINO, Saichi and NAKAMURA, Noboru},
     title = {Maximization of quadratic forms expressed by distance matrices},
     journal = {Hokkaido Math. J.},
     volume = {35},
     number = {1},
     year = {2006},
     pages = { 641-658},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1285766422}
}

IZUMINO, Saichi; NAKAMURA, Noboru. Maximization of quadratic forms expressed by distance matrices. Hokkaido Math. J., Tome 35 (2006) no. 1, pp.  641-658. http://gdmltest.u-ga.fr/item/1285766422/