Question: Given u 0 in R n , let L = Span {u}. For y in R n , the reflection of y in L

Given u ≠ 0 in Rⁿ, let L = Span {u}. For y in Rⁿ, the reflection of y in L is the point refl_L, y defined by

refl, y = 2 proj, y - y

See the figure, which shows that refl_L ŷ = proj_L, y and ŷ - y. Show that the mapping y ↦ refl_L, y is a linear transformation.

The reflection of y in a line through the origin.

refl, y = 2 proj, y - y

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To show that the mapping y reflL y is a linear transformation we need to prove that it satisfies two properties additivity and scalar multiplication Lets consider two vectors y and y in R and a scalar ... View full answer

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