The nth power of rotation through () is rotation through n(): An = [eos() -Sin()]n =

Chapter 6, Problem 36

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The nth power of rotation through () is rotation through n(): An = [eos() -Sin()]n = [cosn() -Sinn()] sin () cos () sin n () cos n () . Prove that neat formula by diagonalizing A = SAS-1 . The eigenvectors (columns of S) are (I, i) and (i, 1). You need to know Euler's formula eiB = cos () + i sin ().

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