2 problems

Let a biquadratic form be a homogeneous polynomial of degree two in each of two variable vectors, and let its SOS rank be the smallest number of squares of bilinear forms in a sum-…

Let $P(\mathbf{x},\mathbf{y})$ be a $3 \times 3$ symmetric PSD biquadratic form, so $P(\mathbf{x},\mathbf{y})\geq 0$ for all $\mathbf{x},\mathbf{y}\in\mathbb{R}^3$. A bilinear form…