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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: 3,110 Thanks: 855  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.  

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computing, inner product, matrix, product 
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