Understanding the Symmetric Matrix Problem: A Brief Overview

[ak123456]

Homework Statement

consider the 2*2 symmetric matrix A =
(a b )
(b c)
and define f: R^2--R by f(x)=X*AX . show that [tex]\nabla[/tex]f(x)=2AX

Homework Equations

The Attempt at a Solution

quiet confuse about this question
[tex]\nabla[/tex]f(x)=(

Homework Statement

consider the 2*2 symmetric matrix A =
(a b )
(b c)
and define f: R^2--R by f(x)=X*AX . show that [tex]\nabla[/tex]f(x)=2AX

Homework Equations

The Attempt at a Solution

quiet confuse about this question
[tex]\nabla[/tex]f(x)=(diff(f, x) , diff(f,y) )
can i set L=(u,v) to prove L is a linear map?

 

[lanedance]

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

[tex] f:\Re^2 \rightarrow \Re [/tex]
[tex] f:\textbf{x}\rightarrow z [/tex] for [tex] \textbf{x}=(x,y) \in \Re^2, z \in \Re[/tex]

with f defined by
[tex] f(\textbf{x}) = z = \textbf{x}^T \textbf{.A.x}[/tex]
if unsure how about multiplying this out based on your matrix?

then what is
[tex]\nabla f(\textbf{x})[/tex]?