Can anyone explain this property to me please? If P is an orthogonal projection matrix, then I - 2P is unitary. Thanks.
Follow Math Help Forum on Facebook and Google+
Originally Posted by Bucephalus Can anyone explain this property to me please? If P is an orthogonal projection matrix, then I - 2P is unitary. Thanks. Let's see: $\displaystyle (I-2P)^{*}=I^{*}-2P^{*}=I-2P^{*}=I-2P$ , since a projection is orthogonal iff it is self-adjoint, and then: $\displaystyle (I-2P)(I-2P)^{*}=(I-2P)(I-2P)==I-4P+4P^2=I$ (why?) $\displaystyle \Longrightarrow I-2P$ is unitary. Tonio
that's awesome. Thanks Tonio
View Tag Cloud