Proving the Frobenius Norm Identity for Matrices

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Homework Help Overview

The discussion revolves around proving the Frobenius norm identity for matrices, specifically the equation ∥A∥F = √trace(ATA), applicable for matrices A in R m×n.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss various methods of proof, including numerical approaches and index notation for the trace function. Some express confusion and seek guidance on how to begin the proof.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and seeking clarification. There is a mix of exploratory questions and suggestions for starting points, but no consensus has been reached yet.

Contextual Notes

Some participants mention feeling lost and request initial guidance, indicating a need for foundational understanding of the concepts involved.

iwan89
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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?
 
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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.
 

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