Does linear transformation, prevent preserve angle between two vectors? I guess that it is true, so if we translate normal vector of a plan, it will be orthogonal to translated plan.
linear transformation and angles?
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$\begingroup$
linear-algebra
transformation
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1@MichaelAlbanese,I,m sorry.I mean `preserve`. – 2012-12-27
2 Answers
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No. Imagine strectching the plane in the $x$-direction. Formally $(x,y)\mapsto (2x,y)$. The angle $(1,1)$ makes with $(1,0)$, which, originally is 45 degrees, is reduced.
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0Thank you for your attention. – 2012-12-27
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Only a subset of linear transformations also preserves angles. Orthogonal transformations preserve length and angles and can easily be characterized. If you want to drop the length condition then also stretching with the same factor along all coordinate axes is allowed. Note that there are also non-linear angle preserving transformations (conformal maps).
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0Thank you. +1 Up vote for your helpful information. – 2012-12-27