Proving a matrix is orthogonal.

  • Thread starter Lucy Yeats
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  • #1
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Homework Statement



Question 10a of the attached paper.


Homework Equations





The Attempt at a Solution



If a matrix is orthogonal, its transpose is its inverse.

The inverse [itex]U^{-1}[/itex] is defined by Ʃ[itex]U^{-1}[/itex]ij Vj = uj

I don't know how to go about proving this. Thanks for any help!
 

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Answers and Replies

  • #2
HallsofIvy
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There is no attached paper! Also your given definition of "inverse" can't be true because it makes no sense- you haven't said what Vj and uj are (and you must mean ui, not uj because you should be summing over j). If you are given a specific matrix, you need to answer three questions:
1) What is its transpose?
2) What is its inverse?
3) Are they the same?
 
  • #3
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I attached the paper about a minute after I posted; I think it's there now. :-)
 
  • #4
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Also, the sum is from j=1 to n. So the ith element of the vector u is the sum of the elements of one row of the matrix U with the elements of the vector j.
 
  • #5
Office_Shredder
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Take the inner product of vi and vj using their expansion in terms of u's, and consider how your answer relates to matrix multiplication
 

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