# Math Help - form of symmetric matrix of rank one

1. ## form of symmetric matrix of rank one

The question is:

Let $C$ be a symmetric matrix of rank one. Prove that $C$ must have the form $C=aww^T$, where $a$ is a scalar and $w$ is a vector of norm one.

(I think we can easily prove that if $C$ has the form $C=aww^T$, then $C$ is symmetric and of rank one. But what about the opposite direction...that is what we need to prove. How to prove this?)

2. ## Re: form of symmetric matrix of rank one

Hey ianchenmu.

Have you tried proof by contradiction? (Assume it has different properties and find a contradiction).