vector in the line across which the reflection is performed, and denotes the dot product of with . Note the formula above can also be written as
:saying that a reflection of across is equal to 2 times the projection of on , minus the vector . Reflections in a line have the eigenvalues of 1, and -1.

Reflection through a hyperplane in n dimensions

More generally, if is a linear subspace and is the orthogonal projection onto , then reflection

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