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Unformatted text preview: that S is orthogonal. Start with S 1 , S 1 = ( PQ ) 1 = Q 1 P 1 , (12) where we have used the well-known property that the inverse of a matrix product is the product of the inverse matrices in reverse order. Next, we replace Q 1 and P 1 by their respective transposes to get S 1 = Q 1 P 1 = Q T P T = ( PQ ) T , (13) where the last equality follows from another well-known property that the trans-pose of a matrix product is the product of the transposed matrices in reverse order. Finally, we use Eq.(1) to replace PQ in Eq.(13), leaving us with S 1 = S T , (14) which establishes the desired result. 2...
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This note was uploaded on 12/19/2010 for the course PHYSICS ph 409 taught by Professor Wilemski during the Fall '10 term at Missouri S&T.
- Fall '10