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##### Rotation matrices

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**Rotation matrices**Constructing rotation matrices Eigenvectors and eigenvalues y x 0**Rotating a vector**y Length v x 0**Repeatedly rotating a vector**y x 0 How can we recognize a rotation matrix? STOP**Rotation matrices**Constructing rotation matrices Eigenvectors and eigenvalues y x 0**Complex eigenvalues and eigenvectors**Please confirm these last 2 lines Complex eigenvalues Complex eigenvectors STOP**Complex eigenvalues and eigenvectors**Complex eigenvalues Complex eigenvectors**Complex eigenvalues and eigenvectors**y Consider an example with w+ = w- = w/2 x 0 In this example, the initial vector points directly to the right. How should the coefficients w+ and w- be changed to represent an initial vector pointing at an arbitrary initial anglerelative to the x axis? Can you plot the eigenvectors (1, ±i) on the xy plane? (No). Why not?