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linear algebra - Elementary reflector $Q$ is orthogonal iff ...
WebMay 26, 2016 · linear algebra - Elementary reflector $Q$ is orthogonal iff - Mathematics Stack Exchange Elementary reflector Q is orthogonal iff Ask Question Asked 6 years, 10 months ago Modified 6 years, 10 months ago Viewed 269 times 0 Recall that an elementary reflector has the form Q = I + α x x T ∈ R n × n with ‖ x ‖ 2 ≠ 0. Show that Q is orthogonal iff WebMar 8, 2015 · If you want to have a more geometrical view of why this is the case, you can prove the following: If ‖ x ‖ = ‖ y ‖, then x + y and x − y bisects the angle between x and y. If ‖ x ‖ = ‖ y ‖ and the vector u bisects the angle between x and y, then the Householder reflector associated to u sends x into y (and vice versa0. haywood county court nc
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