
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 18th, 2017, 06:39 AM  #1 
Newbie Joined: May 2017 From: Essex Posts: 1 Thanks: 0  Computing a matrix according to inner product
Hi I've got an answer to this question, but I'm not sure if it's actually right. If someone could read through and see what they get, that would be a massive help. Thanks. Question: consider the matrix K = (2 0 1; 5 7 0; 3 1 1). Recall the definition of projector operator: P(A)B = A <A, B>/A^2 on a matrix space with inner product <.,.> Compute the matrix: M = (1P(1))K, according to the inner product <A,B> = Tr(A'S'SB) Here 1 is the identity matrix, S is the diagonal matrix with diagonal entries (1,2,1). Also A' means A transpose, I wasn't sure how to write it. And P(A)B for the projector operator is P subscript A, B. So I expanded the brackets and used the projector operator to come to K  1(Tr(1'S'SK))1^2 From there I worked the trace part to be 31, and then norm of the identity to be 6. This meant the matrix M came out to: M = (184 0 1; 5 179 0; 3 1 185) Please help and let me know if I've gone wrong. Last edited by skipjack; May 18th, 2017 at 06:23 PM. 
May 22nd, 2017, 02:56 AM  #2  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894  Quote:
and its transpose is Quote:
Quote:
Yes, that has trace 21. Quote:
Quote:
Last edited by Country Boy; May 22nd, 2017 at 02:58 AM.  

Tags 
computing, inner product, matrix, product 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Computing the CoSkewness matrix  MichaelGong  Economics  2  March 2nd, 2014 01:58 PM 
Minimizing a matrix product  th1j5  Linear Algebra  1  May 15th, 2013 01:17 AM 
matrix and pi product thing  tejolson  Linear Algebra  1  March 24th, 2013 07:41 PM 
Computing Inverse of a Matrix Applications  prashantakerkar  Algebra  6  November 15th, 2011 10:49 PM 
Computing the rank of this matrix quickly?  forcesofodin  Linear Algebra  3  April 16th, 2010 12:30 PM 