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

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Presentation transcript:

Rotation matrices 1 Constructing rotation matricesEigenvectors and eigenvalues 0 x y

2 Rotating a vector 0 x y Length v

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

Rotation matrices 4 Constructing rotation matricesEigenvectors and eigenvalues 0 x y

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

6 Complex eigenvalues and eigenvectors Complex eigenvalues Complex eigenvectors

7 Complex eigenvalues and eigenvectors Consider an example with w + = w - = w/2 0 x y 1.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? 2.Can you plot the eigenvectors (1, ±i) on the xy plane? (No). Why not?