Matrix power to minimize error in neural network using Newton's method

Question

Hello, I have a non square matrix A and i want to know A^2.

Actually i am working in neural network newton optimization method using second order Taylor series such that I want to multiply the hessian matrix H(second derivative) with the square of the weight vectors.

It is written as: Delta(w(n))' * H(n) * Delta(w(n))

Actually it is using the quadratic function but i could not know why.

Thanks.