Lecture Notes (23)

# This function is an example of something well call a

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Unformatted text preview: ors in R2 and maps them to vectors in R2 . This function is an example of something we’ll call a linear map. We can look at speciﬁc vectors like (8) L 1 0 = 2 0 0 3 1 0 = 2 0 , (9) L 0 1 = 2 0 0 3 0 1 = 0 3 , L 1 1 = 2 0 0 3 1 1 = 2 3 . and (10) If you draw the vectors and what they map to, you’ll see that the unit square is being mapped to a rectangle 1 0 stretched by a factor of 2 in the direction and by a factor of 3 in the direction. 0 1 1 MA 3280 Lecture 23 - More on Eigenvectors 2 Something similar is happening in the linear map (11) x1 x2 L 1 −1 2 4 = x1 x2 = x1 − x2 2x1 + 4x2 , although it’s probably not as clear. Note that the matrix is the same one that we found eigenvalues and eigenvectors for. The eigenvectors map as follows. L 1 −1 = 1 −1 2 4 1 −1 = 2 −2 L (12) 1 −2 = 1 −1 2 4 1 −2 = 3 −6 and (13) Here, the mapping stretches by...
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## This document was uploaded on 04/03/2014.

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