Doing an exercise on Matrices.
I am asked to find the rank of the quadratic form $2xy+2yz+2zx$ over $\mathbb R$. I understand that you need to find a diagonal matrix congruent to $\begin{pmatrix} 0&1&1\\ 1&0&1\\ 1&1&0 \end{pmatrix}$ but when I look at the solution it talks about the eigenvalues of this matrix.
What I don't understand is why we are interested in the eigenvalues, since we are looking at the matrix in the context of bilinear forms, as opposed to looking at it as an endomorphism.
So what is the connection here?