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Solution of the quadratic form


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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! >:D

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