Matching method is a method of transforming quadratic form into standard form, and the standard form is f(x 1, x2, x3) = x12-x1x2+x2x3.

First, we need to convert quadratic form into standard form, which requires two steps:

The quadratic form is transformed into the form of the unary quadratic equation, for example, f(x 1, x2, x3) = ax12+bx1x2+cx2x3+dx1+ex2+fx3+g is transformed into f (x/kloc-0).

Then the unary quadratic equation is transformed into the standard form, that is, f(x 1, x2, x3) = x12-x1x2+x2x3+dx1+ex2+fx3+g = 0.

Next, you can write reversible linear transformation, that is, using a series of linear transformations to transform quadratic form into standard form. In order to keep the transformation reversible, we need to ensure that the transformation is orthogonal, that is, it satisfies the orthogonal condition.

Common reversible linear transformations include translation, rotation and scaling. For example, we can translate a quadratic form to the standard position by translation, adjust the direction of a quadratic form to the standard direction by rotation, and adjust the size of a quadratic form to the standard size by scaling.