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Rotation matrices

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.

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Rotation matrices

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  1. Rotation matrices Constructing rotation matrices Eigenvectors and eigenvalues y x 0

  2. Rotating a vector y Length v x 0

  3. Repeatedly rotating a vector y x 0 How can we recognize a rotation matrix? STOP

  4. Rotation matrices Constructing rotation matrices Eigenvectors and eigenvalues y x 0

  5. Complex eigenvalues and eigenvectors Please confirm these last 2 lines Complex eigenvalues Complex eigenvectors STOP

  6. Complex eigenvalues and eigenvectors Complex eigenvalues Complex eigenvectors

  7. 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 angle relative to the x axis? Can you plot the eigenvectors (1, ±i) on the x-y axes? (No). Why not?

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