2.2 Linear Transformation in Geometry Example. 1 Consider a linear ...
2.2 Linear Transformation in Geometry Example. 1 Consider a linear ...
2.2 Linear Transformation in Geometry Example. 1 Consider a linear ...
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Def<strong>in</strong>ition. Shear Let L be a l<strong>in</strong>e <strong>in</strong> R 2 . A<br />
l<strong>in</strong>ear transformation T from R 2 to R 2 is called<br />
a shear parallel to L if<br />
a. T (v) = v, for all vectors v on L, and<br />
b. T (v)−v is parallel to L for all vectors x ∈ R 2 .<br />
<strong>Example</strong>. 7 <strong>Consider</strong> two perpendicular vectors<br />
u and w <strong>in</strong> R 2 . Show that the transformation<br />
T (x) = x + (u · ¯x) w<br />
is a shear parallel to the l<strong>in</strong>e L spanned by w.<br />
6
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