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Having a unitary matrix $X$ whose size is $n \times n$ and a vector $z$ whose length is $n$, and let's have:

$$y = X^H {\rm diag}(z)X$$

where $X^H$ is the conjugate transpose of $X$.

My question, is the complexity of this multiplication is still almost $n^3$ or since the matrix $X$ is unitary, multiplication complexity should be less ?

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  • $\begingroup$ What is H...another unitary matrix? $\endgroup$
    – Dsp guy sam
    May 24, 2020 at 11:51
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    $\begingroup$ I must admit I don't see how this is signal processing? $\endgroup$
    – Marcus Müller
    May 24, 2020 at 14:57
  • $\begingroup$ @Dspguysam .. Sorry I modified it, it's $X$ it's not $H$. $\endgroup$
    – New_student
    May 24, 2020 at 15:20
  • $\begingroup$ @MarcusMüller A computation that sounds quite DSP-like, indeed not in the core business $\endgroup$
    – Laurent Duval
    May 24, 2020 at 18:47

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