Solution of the quadratic form

[ggyyree]

I have got a quadratic form as following:

 

F(w) = g^T * w + (1/2)* w^T * B * w

 

Here T is the matrix transpose. Someone said the if p is a solution to this quadratic form then p is a solution to an equation of the form:

 

(B + aI) * p = -g

 

Here I is the identity matrix.

 

May I ask why please? Thanks a lot!