Proving the Frobenius Norm Identity for Matrices

iwan89
Messages
27
Reaction score
0

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?
 
Physics news on Phys.org
The product AT A worked out gives the sum of all entries squared.
 
Can you give me a head start? :( I am in total lost :(
 
iwan89 said:
Can you give me a head start? :( I am in total lost :(

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

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Proving the Frobenius Norm as a Matrix Norm
Replies
2
Views
3K
Proving statements about matrices | Linear Algebra
Replies
25
Views
3K
Question about the Frobenius method and Bessel functions
Replies
4
Views
2K
Solving differential equation (t^2-1)y''-6y=1
Replies
2
Views
770
Constructing a cube with a Norm
Replies
1
Views
2K
Prove that range ##T'## = ##(\text{null}\ T)^0##
Replies
1
Views
1K
Finding roots in an extension field
Replies
7
Views
2K
Solve Equation with Method of Frobenius
Replies
4
Views
2K
Do these two statements imply an underlying induction proof?
Replies
7
Views
1K
Proving isomorphisms [Linear Algebra]
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top