How do I solve this matrix?

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

• I have added the equations for you. – Théophile Jan 7 '15 at 21:39
• Here is an excellent reference, by the way, for learning how to typeset these kinds of things: MathJax basic tutorial – Théophile Jan 7 '15 at 21:42
• @DietrichBurde there are many Toms in this world – Omnomnomnom Jan 7 '15 at 21:57
• 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. – Omnomnomnom Jan 7 '15 at 22:02
• @Theophile thanks a lot! – Tom Jan 7 '15 at 23:20