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Math Help - [SOLVED] Projection matrix property

  1. #1
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    [SOLVED] Projection matrix property

    Can anyone explain this property to me please?

    If P is an orthogonal projection matrix, then I - 2P is unitary.

    Thanks.
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  2. #2
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    Quote Originally Posted by Bucephalus View Post
    Can anyone explain this property to me please?

    If P is an orthogonal projection matrix, then I - 2P is unitary.

    Thanks.

    Let's see: (I-2P)^{*}=I^{*}-2P^{*}=I-2P^{*}=I-2P , since a projection is orthogonal iff it is self-adjoint, and then:

    (I-2P)(I-2P)^{*}=(I-2P)(I-2P)==I-4P+4P^2=I (why?) \Longrightarrow I-2P is unitary.

    Tonio
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  3. #3
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    that's awesome.
    Thanks Tonio
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