My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 15th, 2011, 06:37 AM   #1
Newbie
 
Joined: May 2011

Posts: 2
Thanks: 0

Frobenius norm

Hello,

I am a newbie to this Forum.
I would to ask you about Frobenius Norm?
What is its utility. What it is measuring (not the formula, but the its meaning).

Thank you.
Maissa is offline  
 
May 15th, 2011, 08:24 AM   #2
Senior Member
 
Joined: Jun 2010

Posts: 618
Thanks: 0

Re: Frobenius norm

Maissa,

Welcome to the forum.

The Frobenius norm is the -norm on the space of matrices of a given shape. In other words, you interpret the matrix as a large vector, and compute the norm in the usual Euclidean way. I suppose that since this norm is expressed solely in terms of the entries of the matrix, it is appealing for applications. I believe it is "sub-multiplicative", meaning it satisfies



which can be a good property to have.

As for what it means, it is merely a way to assign a size to a matrix. There are other good norms for matrices, all with slightly different properties and optimal uses. Did you have some specific property of the Frobenius norm as compared to other norms in mind with this question?

-Ormkärr-
 is offline  
May 29th, 2011, 02:25 AM   #3
Newbie
 
Joined: May 2011

Posts: 2
Thanks: 0

Re: Frobenius norm

Hi,
I am very thankful
Maissa is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
frobenius, norm



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
fixed field of frobenius-automorphism Sandra93 Abstract Algebra 2 January 5th, 2014 11:18 AM
Frobenius coin problem-induction rayman Algebra 5 May 26th, 2013 01:02 AM
Frobenius theorem Fernando Abstract Algebra 1 February 24th, 2012 06:43 AM
Frobenius method zokomoko Applied Math 0 June 14th, 2010 07:38 AM
Differential equations, method of frobenius silentwf Differential Equations 0 April 12th, 2010 05:08 AM





Copyright © 2017 My Math Forum. All rights reserved.