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 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. February 26th, 2016, 05:22 PM #2 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 What have you tried so far? 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 can´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. February 27th, 2016, 01:23 PM #4 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 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*|| 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! Tags norm, vectorial Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post FunWarrior Linear Algebra 0 February 11th, 2014 01:22 AM bvh Advanced Statistics 0 May 9th, 2013 11:29 PM libo Linear Algebra 1 January 30th, 2012 05:21 PM praveen97uma Linear Algebra 4 May 9th, 2010 01:40 PM lobstertail Advanced Statistics 0 April 17th, 2009 11:33 AM

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