Indefinite Form

a concept in linear algebra. The quadratic form

with real coefficients a, _ij is called an indefinite form if it takes on positive and negative values for real values of the variables. By a linear change of variables, we can reduce an indefinite quadratic form to a form

For a given indefinite form the values of s and t are independent of the method of reduction of that form to the form (*) (this result is called the law of inertia of quadratic forms). The indefinite form

x² + y² + z² − c²t²

plays an important role in special relativity. Indefinite quadratic forms occur in the study of extrema of functions of several variables, in mechanics, and in analytic geometry.