Please answer from a Linear Algebra standpoint. Let u be a unit vector in C^n and let U = I - 2uuH. Show that U is both unitary and Hermitian and is therefore its own inverse.
Added by Dylan A.
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A matrix is unitary if its conjugate transpose is equal to its inverse, i.e., UU^H = I. U^H = (I - 2uu^H)^H = I^H - (2uu^H)^H = I - 2(uu^H)^H = I - 2u^Hu^H Now, let's compute UU^H: UU^H = (I - 2uu^H)(I - 2u^Hu^H) = I - 2uu^H - 2u^Hu^H + 4(uu^H)(u^Hu^H) Since u Show more…
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