My Math Forum The projection of a vector over the orthogonal subspace of other.

 Linear Algebra Linear Algebra Math Forum

 April 15th, 2018, 08:46 AM #1 Newbie   Joined: Jan 2018 From: brazil Posts: 4 Thanks: 0 The projection of a vector over the orthogonal subspace of other. Hello I have the vector B = (2,4,1) and want to project it over the orthogonal subspace of another vector, the vector A = (1,1-1). I did: (1,1,-1).(2,4,-1) * (1,1,-1) = $\displaystyle 7/3 * (1,1,-1) = (7/3,7/3,-7/3)$ (1,1,-1).(1,1-1) and then : $\displaystyle (7/3,7/3,-7/3) - (2,4,1) = (7/3,7/3,-7/3) - (6/3,12/3,3/3) = (1/3,-5/3,-10/3)$ Nonetheless, the correct answer it is: $\displaystyle (1/3,7/3,8/3)$. So what I am doing wrong? Thanks for the input.
 April 15th, 2018, 02:15 PM #2 Global Moderator   Joined: May 2007 Posts: 6,849 Thanks: 742 Your first calculation has an error. You used (2,4,-1) instead of (2,4,1). If you do it correctly, you will get the correct answer with a minus sign. This is because your final subtraction is opposite the usual definition. Thanks from coltson

 Tags orthogonal, projection, subspace, vector

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post atraxis Applied Math 6 June 16th, 2015 03:31 AM david940 Linear Algebra 1 June 27th, 2014 07:46 AM atraxis Algebra 0 November 24th, 2013 08:15 AM Robertoo Linear Algebra 3 January 5th, 2013 08:58 AM abcdefg Algebra 1 September 27th, 2011 05:35 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top