Form of symmetric matrix of rank one

[ianchenmu]

Homework Statement

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.

Homework Equations

n/a

The Attempt at a Solution

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?

 

[Dick]

Homework Statement

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.

Homework Equations

n/a

The Attempt at a Solution

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?

Do you know that if C is symmetric, it can be diagonalized?