Let A be an invertible real n × n matrix. Define a function F : ℝn × ℝn → ℝ by F(x, y) = 〈Ax, y〉 where 〈x, y〉 where (x, y) denotes the inner product of x and y. Let DF(x, y) denote the derivative of F at (x, y) which is a linear transformation from ℝn × ℝn → ℝ. Then