Elements of Numerical Mathematical Economics with Excel

3.4. Quadratic forms and definiteness of a symmetric matrix

Another important problem of linear algebra and economic applications is represented by the quadratic form, which is given by the following expression:

Q ( x ) = ∑ i = 1 n ∑ j = 1 n a i j x i x j ,

(3.4-1)

or, in a complete extended form, by the following:

{ a 11 x 1 x 1 + a 12 x 1 x 2 + ⋯ + a 1 j x 1 x j + ⋯ + a 1 n x 1 x n + + a 21 x 2 x 1 + a 22 x 2 x 2 + ⋯ + a 2 j x 2 x j + ⋯ + a 2 n x 2 x n + ⋯ + a i 1 x i x 1 + a i 2 x i x 2 + ⋯ + a i j