(1) Explain how to modify the definition of the Householder reflect...

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(1) Explain how to modify the definition of the Householder reflector SO that it works for a vector with complex entries. That is, given x € Cm, how should we define the unit vector U and the phase eil, so that (Id- 22v** = eillialles? (2) If P: Rm Rm is an orthogonal projection of rank k < m, then find a basis for Rm in which the action of the reflection R.P = Id - 2P is as simple as possible, and explain what that is. What is det R.P?

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