On positive definite biquadratic forms irreducible to sums of squares of bilinear forms (Q1358180)

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.