2. If it is irreversible, it cannot be transformed into coordinate transformation, so the positive and negative inertia index of the standard line obtained by matching method can be changed. The coordinate transformation of postgraduate entrance examination does not change the positive definiteness of quadratic form.

Quadratic form: a quadratic polynomial with n variables is called quadratic form, that is, in a polynomial, the number of unknowns is arbitrary, but the degree of each term is 2. Given this definition, the number of unknowns is arbitrary, so the number of each term is 2.

Behind the quadratic form

Quadratic form, in which every term is quadratic, the value of the first row and the second column is half of the coefficient of x 1x2, which is very important. When using this concept when doing problems, we should pay special attention to writing the right matrix, otherwise it is wrong to find the eigenvalues and eigenvectors.

Secondly, canonical form and canonical form, canonical form: if quadratic form has only square terms and no mixed terms (that is, the coefficients of mixed terms are all zero), then we call quadratic form canonical form, also called sum of squares. Standard form: in the standard form of quadratic form, if the coefficient d of the square term is only 1,-1, 0, it is called the standard form of quadratic form.