
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 18th, 2018, 08:13 PM  #1 
Newbie Joined: Apr 2018 From: British Posts: 2 Thanks: 0  Projection onto eigenspace
Hi, there is a question from my review sheet. A= 2 i i 2 Let T = LA be a linear transformation, use the standard inner product space on C2. (a) Find the projections T1, T2 onto the eigenspaces of T. (b) Show T 1 as the combination of these projections. I am confused with what does the projection onto eigenspace mean. How can I find it? Use GramSch Process? Thanks 
April 20th, 2018, 09:33 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,244 Thanks: 885 
You say you do not know what "projection onto eigenspace" means? Okay, do you know what and "eigenspace" is? Do you know what a "projection" is? The eigenspace of a Linear transformation is the subspace spanned by its eigenvectors. Have you found the eigenvalues of T? Have you found the eigenvectors corresponding to each of those eigenvalues? The projection of vector v onto a subspace S is the vector u in S such that vu is orthogonal to S. 

Tags 
eigenspace, projection 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Linear Algebra  Eigenspace  PlzzHelp  Linear Algebra  1  May 13th, 2016 04:28 AM 
Please help to find a basis of eigenspace  JORGEMAL  Linear Algebra  1  November 29th, 2014 09:01 PM 
projection?  xzardaz  Linear Algebra  0  February 3rd, 2012 03:47 AM 
Relation of eigenspace in solving Ax=b  RobertT  Linear Algebra  0  February 3rd, 2011 10:52 AM 
About projection  redox  Algebra  0  April 26th, 2009 10:37 AM 