Linear transformations and eigenvectors in 2D

This worksheet illustrates the effect of a linear transformation in [math]R^2[/math] on the unit circle/unit disk, and the geometric meaning of eigenvectors, eigenvalues and determinant. Students can drag a point on the unit circle and its image under the transformation will automatically update. Students can geometrically identify the eigenvectors by observing when the vector and its image are parallel, and the eigenvalues by their relative lengths. The effect of the transformation as a geometrical transformation can be illustrated by clicking 'Show clockface'. This will animate the effect of the transformation on the unit disk (shown as a clockface). Eigenvectors can be identified geometrically as the axes of dilation or reflection. The image of the standard basis vectors [math]e_1 = (1,0), e_2 = (0,1)[/math] under the transformation can also be shown. These images are the columns of the transformation matrix. The transformation can be changed by dragging the standard basis image points, or by entering a new matrix T numerically.



Resource Type
Target Group (Age)
18 – 19+
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