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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 wellknown 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 wellknown property that the transpose 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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 Fall '10
 Wilemski
 Linear Algebra, mechanics, Invertible matrix, Pik Qkl Rlj, Pik Tkj, Pil Qlk Rkj

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