Proving the Frobenius Norm Identity for Matrices

[iwan89]

Homework Statement

Prove ∥A∥F =√trace(ATA), for all A ∈ R m×n

Where T= transpose

Homework Equations

The Attempt at a Solution

I tried and i just can prove it by using numerical method. Is there anyway to prove the equation in a correct way?

 

[dirk_mec1]

The product AT A worked out gives the sum of all entries squared.

 

[iwan89]

Can you give me a head start? :( I am in total lost :(

 

[Dick]

Can you give me a head start? :( I am in total lost :(

Write trace(AA^T) out in index notation.