Assuming that shrinking/expanding in a given direction is a linear transformation in [itex]R^3[/itex], what would be the matrix to perform it?(adsbygoogle = window.adsbygoogle || []).push({});

To be more precise, given a vector

[tex]e=\left(\begin{array}{c}e_1\\e_2\\e_3\end{array}\right)[/tex]

with a length of 1, i.e. [tex]||e||=1[/tex] and a factor [itex]\lambda[/itex], I am looking for a matrix [itex]A[/itex] such that for every vector x the vector [itex]y=A\cdot[/itex]x has a projection on e that is longer than the projection of x by the factor [itex]\lambda[/itex], while all sizes orthogonal to e are kept unchanged.

I came up with a matrix [itex]A[/itex] that contains squares and products of the [itex]e_i[/itex] and, worse, would contain complex numbers for [itex]\lambda<1[/itex]. I expected something simpler? Any ideas?

Thanks,

Harald.

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# Linear Transformation to Shrinking/Expand along a given direction

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