My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 26th, 2016, 01:50 PM   #1
Newbie
 
Joined: Feb 2016
From: Montevideo

Posts: 3
Thanks: 0

Vectorial norm help

Hello, I am new to the forums. I was not sure if this question should be asked in this section, but as the exercise is from my calculus course I have posted it here. Here is the question:
Does the function ||(x,y)||=max{|x+y|,|x-y|} define a function in R2?

I am having trouble in proving (or disproving) the triangle inequality.

Thank you in advance for your help.
juanpe966 is offline  
 
February 26th, 2016, 05:22 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,730
Thanks: 689

What have you tried so far?
mathman is offline  
February 26th, 2016, 08:51 PM   #3
Newbie
 
Joined: Feb 2016
From: Montevideo

Posts: 3
Thanks: 0

Correction: It should say define a NORM in R2*

What I have tried:
I want to prove that ||(x,y)+(x*,y*)||=<||(x,y)||+||(x*,y*)||
I know that: ||(x,y)+(x*,y*)||=max{|(x+y)+(x*+y*)|,|(x-y)+(x*-y*)|}

I know from absolute value properties that:
|(x+y)+(x*+y*)|=<|(x+y)|+|(x*+y*)| and
|(x-y)+(x*-y*)|=<|(x-y)|+|(x*-y*)|

Now, the problem I have is the following:
Lets say that ||(x,y)+(x*,y*)||=|(x+y)+(x*+y*)|=<|(x+y)|+|(x*+y* )|
What I would need to prove is that:
||(x,y)||=|(x+y)| and
||(x*,y*)||=|(x*+y*)|

My doubt is that why canĀ“t it be that ||(x,y)||=|(x-y)| in the even though
|(x+y)+(x*+y*)|>|(x-y)+(x*-y*)|.
In other words, can I be certain that if |(x+y)+(x*+y*)|>|(x-y)+(x*-y*)| then |(x+y)|>|(x-y)| and |(x*+y*)|>|(x*-y*)| and the same for the other case? If I can prove that then the problem is done.
juanpe966 is offline  
February 27th, 2016, 01:23 PM   #4
Global Moderator
 
Joined: May 2007

Posts: 6,730
Thanks: 689

I am confused about your doubt.

There are 2 cases:

||(x,y)+(x*,y*)||=|(x+y)+(x*+y*)|=<|(x+y)|+|(x*+y* )|=<|||x,y||+||x*,y*||
||(x,y)+(x*,y*)||=|(x-y)+(x*-y*)|=<|(x-y)|+|(x*-y*)|=<|||x,y||+||x*,y*||
mathman is offline  
February 27th, 2016, 02:24 PM   #5
Newbie
 
Joined: Feb 2016
From: Montevideo

Posts: 3
Thanks: 0

Actually, maybe you did not understand me but you wrote exactly what I needed. I was writing a reply and then it clicked, maybe I was confusing myself, looking for a problem when there was not one (classic math).

You may not know how you helped, but you did. I am truly grateful

Cheers!
juanpe966 is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
norm, vectorial



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Non-linear vectorial equation FunWarrior Linear Algebra 0 February 11th, 2014 01:22 AM
inequality with norm bvh Advanced Statistics 0 May 9th, 2013 11:29 PM
Norm libo Linear Algebra 1 January 30th, 2012 05:21 PM
What is the norm of (1,0,i)? praveen97uma Linear Algebra 4 May 9th, 2010 01:40 PM
PDF of the 2-norm lobstertail Advanced Statistics 0 April 17th, 2009 11:33 AM





Copyright © 2019 My Math Forum. All rights reserved.