I have three (N x 1) complex vectors,(adsbygoogle = window.adsbygoogle || []).push({}); a,bandc.

I know the following conditions:

(1)aandbare orthonormal (but length ofcis unknown)

(2)clies in the same 2D plane asaandb

(3)a^{H}c= x (purely real, known)

(4)b^{H}c=iy (purely imaginary, unknown)

where (.)^{H}denotes Hermitian (conjugate) transpose,iis the imaginary unit and x,y are real numbers.

Given that I know x, can I deduce y?

My hunch is that (without the "purely real/imaginary" statements), these conditions would define y up to an arbitrary complex phase, but the "purely real/imaginary" conditions allow the phase to be known too. However, my reasoning relies on there being some sense of "angle" betweenaandcand betweenbandc... such that these angles sum to 90° for the orthonormality condition (1). I don't know if this is valid.

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# Homework Help: Inner product of complex vectors

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