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.