# Symmetric matrix problem

1. Mar 18, 2009

### ak123456

1. The problem statement, all variables and given/known data
consider the 2*2 symmetric matrix A =
(a b )
(b c)
and define f: R^2--R by f(x)=X*AX . show that $$\nabla$$f(x)=2AX

2. Relevant equations

3. The attempt at a solution
$$\nabla$$f(x)=(1. The problem statement, all variables and given/known data
consider the 2*2 symmetric matrix A =
(a b )
(b c)
and define f: R^2--R by f(x)=X*AX . show that $$\nabla$$f(x)=2AX

2. Relevant equations

3. The attempt at a solution
$$\nabla$$f(x)=(diff(f, x) , diff(f,y) )
can i set L=(u,v) to prove L is a linear map?

2. Mar 18, 2009

### lanedance

Re: question

I think it could be your notation, do you mean:

$$f:\Re^2 \rightarrow \Re$$
$$f:\textbf{x}\rightarrow z$$ for $$\textbf{x}=(x,y) \in \Re^2, z \in \Re$$

with f defined by
$$f(\textbf{x}) = z = \textbf{x}^T \textbf{.A.x}$$
$$\nabla f(\textbf{x})$$?