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?