matrix transformations

Bob

2005-05-15 18:09:54 UTC

Post by BarryAC
I have a query about the 2x2 square matrix operator where a = -1, b = 0, c =
0, and d = -1. I have found it described in a textbook here in the Caribbean
(Greer & Layne, "Certificate Mathematics", Nelson Thornes 2001) as a
reflection through the origin (a point). I thought this operator was an
enlargement, scale factor -1, or it could also be a rotation about the
origin of 180 deg. Can it be a reflection, as there is no lateral
inversion? This same transformation can also be produced by a reflection in
the
x-axis followed by a reflection in the y-axis, and surely a second
reflection always reverses (inverts?) the lateral inversion of the first
reflection? Which is correct, or are they both correct? Kind regards, Barry
AC.

It doesn't really matter what you call it, so long as you know what's
going on. Sometimes it's called a 'reflection in a point', but as you
say, such a reflection is a direct isometry, unlike reflections in lines
or planes etc. FWIW I prefer not to call such a transformation a
reflection, for the reasons you cite. But others do call it a
reflection, so it may be as well to let students know that.

BTW, shouldn't that be 'a relection *in* the origin'? Tricky little
buggers these prepositions, but it's nice to be consistent.

Bob