A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A = a_(i j) is given by Q(x_1, x_2, ..., x_n) = a_(i j) x_i x_j, where Einstein summation has been used. Letting x be a vector made up of x_1, ..., x_n and x^T the transpose, then Q(x) = x^T A x, equivalent to Q(x) = 〈x, A x〉 in inner product notation.

disconnected form | indefinite quadratic form | inner product | integer-matrix form | positive definite quadratic form | positive semidefinite quadratic form | quadratic | quadratic form rank | quadratic form signature | Sylvester's inertia law