I have already aware of the bilinear form of a function which is:
$$<x,y> =x^tAy= \sum_{i,j} a_{ij} x_i y_j$$
Applying this concept to an example:
$$ α(x,y)= \ x^T \begin{bmatrix} 2 & -1 \\ -1 & 1 \\ \end{bmatrix} y $$
Assuming
$$x = \begin{pmatrix} x_1 & y_1 \end{pmatrix}$$
and
$$y = \begin{pmatrix} x_2 \\ y_2 \end{pmatrix}$$ Solving the equation yields:
$$ α(x,y) = 2 x_1 x_2 - y_1 y_2 -x_1 y_2 + y_1 y_2 $$
Now from this information how to ascertain whether the function is bilinear or not? I will really appreciate any help.