The question is:
Let [itex]C[/itex] be a symmetric matrix of rank one. Prove that [itex]C[/itex] must have the form [itex]C=aww^T[/itex], where [itex]a[/itex] is a scalar and [itex]w[/itex] is a vector of norm one.
The Attempt at a Solution
I think we can easily prove that if [itex]C[/itex] has the form [itex]C=aww^T[/itex], then [itex]C[/itex] is symmetric and of rank one. But what about the opposite direction...that is what we need to prove. How to prove this?