Examine transformation properties of functions under symmetry operations I need help learn how t

Jessica Collier

Jessica Collier

Answered question

2022-02-12

Examine transformation properties of functions under symmetry operations
I need help learn how to examine transformation of a functions under a symmetry operation. For example, applying reflection in x axis on a vector (x,y)
(x,y).[1001]=(x,y)
from which we know how x and y transform under reflection. My question is how to examine what happens to other functions such as x2,xy,x2+y2.. etc, under the same operation? Also, how to find matrix representations of the operation for these functions?

Answer & Explanation

skullsxtest7xt

skullsxtest7xt

Beginner2022-02-13Added 15 answers

In this case the simple way is to just replace y with -y in each of those.
However, it worth learning this sooner or later, for more complicated transformations.
xTAx can represent these quadratics.
(xy)(1000)(xy)=x2
(xy)(012120)(xy)=xy
etc. Note that A is symmetric.
Now to transform (x,y) replace
(xy) with (xy)(1001) and (xy) with (1001)T(xy)

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