/sci/ - Science & Math

>>1257599
(1 -2
4 -7)

Your line consists of points (x, mx), so you have an equation
<span class="math">N(x,mx)^T = (x, -mx)[/spoiler], right?

(-1 2
-4 7)

>>1257605
/thread

>>1257605
written out that means you get the equations
x - 2mx = x
4x -7mx = -mx

The first equation is equivalent to -2mx = 0 for all x, thus m = 0, which inserted into the first equation yields x=0 for all x, so there's no value of m for which this works.
Unless I'm mistaken and mirroring (x,mx) on the x-axis doesn't yield (x,-mx). But I think it should since that's just complex conjugation in a sense.

>>1257621
thus m = 0, which inserted into the *SECOND equation

>>1257621
>>1257605
could someone confirm that I'm not talking bullshit?

>>1257635
this is /magnets/. nobody here even knows what you're talking about.

>>1257621

op here, it's along the right lines, but you need to form a quadratic involving m somewhere along the lines, and solve with 2 solutions.. confident that there is a value for m that works

N has positive determinant and therefore maps points in the upper half plane into itself (same for the lower half plane and the x axis). Therefore the only line that can be reflected over the x axis is the x axis itself.

http://en.wikipedia.org/wiki/Poincare_half_plane#Symmetry_groups

also, horse cawk

>>1257657
so (x,0) is the only possible line, now we get:
<span class="math">N(x,0)^T = (x, 4x)^T[/spoiler]
which shows that indeed no value for m can work.

>>1257595
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