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 ?

  • $\begingroup$ What is H...another unitary matrix? $\endgroup$ May 24, 2020 at 11:51
  • 1
    $\begingroup$ I must admit I don't see how this is signal processing? $\endgroup$ May 24, 2020 at 14:57
  • $\begingroup$ @Dspguysam .. Sorry I modified it, it's $X$ it's not $H$. $\endgroup$ May 24, 2020 at 15:20
  • $\begingroup$ @MarcusMüller A computation that sounds quite DSP-like, indeed not in the core business $\endgroup$ May 24, 2020 at 18:47


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.