June 11th, 2018, 04:07 PM  #1 
Newbie Joined: Jun 2018 From: Brazil Posts: 1 Thanks: 0  Invariant Subspaces
Let P be the (hermitian) projection operator onto a subspace M. Show that 1 − P projects onto M⊥. Hint: You need to show that <mPa> = <ma> for arbitrary a> ∈ V and m> ∈ M; therefore, consider (<mPa>)∗, and use the hermiticity of P. 

Tags 
invariant, subspaces 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Sum of two invariant subspaces  Birgitta  Linear Algebra  5  May 14th, 2018 08:27 AM 
Invariant Theory  raul21  Math  1  May 28th, 2014 03:03 AM 
Is connectedness an homotopy invariant?  HubertM  Real Analysis  1  January 19th, 2014 01:19 PM 
A question about topological invariant  hosseinpnt  Real Analysis  3  December 21st, 2012 10:28 AM 
invariant subspace  tinynerdi  Linear Algebra  0  April 11th, 2010 10:48 PM 