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## Homework Statement

V is a n-dimensional euclidean space. U and W are n-1 dimensional subspaces of V.

U and W define a reflection (because of their property as n-1 dimensional subspaces).

Show that

[tex]s_U \circ s_W = s_W \circ s_U[/tex]

if and only if

[tex]W^{\perp}, U^{\perp}[/tex]

are perpendicular.

## Homework Equations

[tex]W^{\perp}[/tex] is the subspace of V such that every vector in [tex]W^{\perp}[/tex] is perpendicular to W.