
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 2nd, 2010, 11:44 PM  #1 
Senior Member Joined: Nov 2009 Posts: 129 Thanks: 0  orthonogonal complement
Let B be a basis for subspace W of an inner product space V, and let z in V. Prove that z in W? if and only if <z.v>=0 for every v in B. => If z in W? then <z,v> = 0 by definition of orthonogonal complement, W? = {z in V: <z,v> = 0 for all v in W} 
May 3rd, 2010, 07:53 AM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: orthonogonal complement
Just look at the definition of a basis, and you should be there.


Tags 
complement, orthonogonal 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A sets complement  WWRtelescoping  Algebra  3  February 18th, 2014 11:15 AM 
p (B intersect (A complement))  finalight  Algebra  1  March 27th, 2012 12:34 PM 
Complement of Whole Space  lu5t  Real Analysis  3  May 31st, 2011 09:36 PM 
complement of sets  Ben92  Applied Math  1  February 7th, 2011 07:19 AM 
the complement of a simple graph  spellbinder  Applied Math  3  October 11th, 2010 03:13 PM 