an:01027892
Zbl 0886.11022
Matyukhin, D. V.
On positive definite biquadratic forms irreducible to sums of squares of bilinear forms
EN
Mosc. Univ. Math. Bull. 50, No. 2, 28-32 (1995); translation from Vestn. Mosk. Univ., Ser. I 1995, No. 2, 29-33 (1995).
00031140
1995
j
11E76 11E39
biquadratic form; bilinear form; quadratic form; open set; sum of squares
The paper considers positive definite biquadratic forms
\[
\sum_{i,j=1}^{n} \sum_{\alpha,\beta=1}^{\mu} f_{ij}^{\alpha \beta}\xi ^{i}\xi ^{j}\eta _{\alpha}\eta _{\beta}. \tag{1}
\]
For \(n>2\), \(\mu >2\), \textit{F. J. Terpstra} [Math. Ann. 116, 166-180 (1938; Zbl 0019.35203)] constructed an example of a form (1) which cannot be represented as the sum of squares of bilinear forms. The present paper generalizes this result by applying Terpstra's construction and proves that if \(n>2\), \(\mu >2\) then there exists an open set of such forms in the space of biquadratic forms.
G.Gogishvili (Tbilisi)
Zbl 0019.35203