| Tartalmi leírás: |
The open problem of determining the exact value of
the n-th linear polarization constant cn of Rn has received considerable
attention over the past few years. This paper makes a contribution
to the subject by providing a new lower bound on the value
of supkyk=1 | hx1, yi · · · hxn, yi |, where x1, . . . , xn are unit vectors
in Rn. The new estimate is given in terms of the eigenvalues of the
Gram matrix [hxi, xji] and improves upon earlier estimates of this
kind. However, the intriguing conjecture cn = n
n/2 remains open.
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