2
$\begingroup$

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.

$\endgroup$
2
  • 1
    $\begingroup$ Do you mean preserve instead of prevent? $\endgroup$ Dec 27, 2012 at 11:30
  • 1
    $\begingroup$ @MichaelAlbanese,I,m sorry.I mean preserve. $\endgroup$ Dec 27, 2012 at 11:33

2 Answers 2

5
$\begingroup$

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).

$\endgroup$
1
  • $\begingroup$ Thank you. +1 Up vote for your helpful information. $\endgroup$ Dec 27, 2012 at 12:16
4
$\begingroup$

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.

$\endgroup$
1
  • $\begingroup$ Thank you for your attention. $\endgroup$ Dec 27, 2012 at 12:06

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .