Lecture Notes (23)

Lecture Notes(23)

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Unformatted text preview: rsing the 0 1 direction. This ﬂips everything upside-down. HW: We have eigenvalues λ = 1, −1, and representative eigenvectors are 3 1 direction, vectors are being held ﬁxed, and in the −5 −2 reversed. It’s not exactly a mirror image, though. Can you picture it? that in the 2) We have eigenvalues λ = 1, 2 and representative eigenvectors ﬁxed in the 3 −1 3 −1 and direction, and being stretched by a factor of 2 in the 3 −5 and 1 −2 . This means direction the vectors are being 2 . Things are being held −1 2 direction. −1 3) The vectors are being rotated by 90◦ in the clockwise direction. 4) No. No vector is being mapped to a scalar multiple image of itself. All vectors map to a vector pointing in a diﬀerent direction. 5) You would solve to rotations. −λ −1 1 −λ = λ2 +1 = 0. This has no real solutions. Imaginary solutions will correspond...
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This document was uploaded on 04/03/2014.

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