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).[100−1]=(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?

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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).[100−1]=(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?

skullsxtest7xt · Accepted Answer

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)(100−1) and (xy) with (100−1)T(xy)

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

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