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How do I expand the following matrix? I have no experience in linear algebra (well 35 years ago..)

Its the equation just after equation 16b in this link


Here are the equations in question:

$$ \begin{bmatrix} Y_m(n) \\ {Y^*}_{-m}(n) \\ \end{bmatrix} = {K_m}^{-1}$$

$$ \begin{bmatrix} Z_m(n) \\ {Z^*}_{-m}(n) \\ \end{bmatrix} = {K_m}^{-1}{K}_m\begin{bmatrix} Y_m(n) \\ {Y^*}_{-m}(n) \\ \end{bmatrix} $$

Where $$ K_m = \begin{bmatrix} K_{1m} & K_{2m}\\ K_{2m}^* & K_{1m}^* \end{bmatrix} $$

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  • $\begingroup$ I have added the equations for you. $\endgroup$ – Théophile Jan 7 '15 at 21:39
  • $\begingroup$ Here is an excellent reference, by the way, for learning how to typeset these kinds of things: MathJax basic tutorial $\endgroup$ – Théophile Jan 7 '15 at 21:42
  • $\begingroup$ @DietrichBurde there are many Toms in this world $\endgroup$ – Omnomnomnom Jan 7 '15 at 21:57
  • $\begingroup$ Perhaps. I think it is safe, for now, to exclude those that were non-existent, or otherwise hindered in the study of linear algebra, 35 years ago. $\endgroup$ – Omnomnomnom Jan 7 '15 at 22:02
  • $\begingroup$ @Theophile thanks a lot! $\endgroup$ – Tom Jan 7 '15 at 23:20

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