Editing Quadratic form (section)

== Equivalence of forms ==
Every quadratic form {{math|''q''}} in {{math|''n''}} variables over a field of characteristic not equal to 2 is [[Matrix congruence|equivalent]] to a '''diagonal form'''
<math display="block">q(x)=a_1 x_1^2 + a_2 x_2^2+ \cdots +a_n x_n^2.</math>

Such a diagonal form is often denoted by {{math|{{angbr|''a''<sub>1</sub>, ..., ''a''<sub>''n''</sub>}}}}.
Classification of all quadratic forms up to equivalence can thus be reduced to the case of diagonal forms.