stylistic:style_transfer
Example

Consider the case of quadratic forms in three variables x, y, z. The matrix A has the form

The above formula gives

So, two different matrices define the same quadratic form if and only if they have the same elements on the diagonal and the same values for the sums b + d, c + g and f + h. In particular, the quadratic form q is defined by a unique symmetric matrix

This generalizes to any number of variables as follows.