Air Play using a raspberry pi

Instructions specific to OS X:

1. Download the image for Raspbian from : raspberrypi.org/downloads.

2. Install this image on the SD card using the app : app for macbook

3. Connect the raspberry pi (RPi) to your router with an ethernet cable and you should be able to ssh into it with the ip form the router's config page, which is 10.0.0.9 for me.

3. Enable wifi so that the RPi can use the WiFi Dongle. Also setup the RPi to receive DLNA content : Stephen Philips Blog

4. Connect the RPi to you speakers and install BubbleUPnP app on android to be able to play music form your phone including from mobile apps like Google Music.

5. Install a media server that streams media over the network. Now to be able to discover your RPi on the network and push DLNA content to it you would have to install another software. I Installed Plex and LINNOSS (Kinsky) to play music from my computer.

Enjoy wire-free music!

Vandermonde Matrix

I was recently trying to prove that a Vandermonde type of matrix is full rank and a quick google search did not give me the the proof I had in mind. So here it is,

Consider a matrix of the form,
\begin{equation}
\begin{bmatrix}
1& \alpha_1& \alpha_1^2& \ldots& \alpha_1^{r-1}\\
1& \alpha_2& \alpha_2^2& \ldots& \alpha_2^{r-1}\\
\vdots \\
1& \alpha_r& \alpha_r^2& \ldots& \alpha_r^{r-1}\\
\end{bmatrix} = [\mathbf{a_0} \ldots \mathbf{a_{r-1}}]
\end{equation}

If this matrix is not full rank then there exists coefficients $c_0, c_1, c_2, \ldots, c_{r-1}$ such that $\sum_i c_i \mathbf{a_i} = \mathbf{0}$. Therfore  there exist $r$ roots $\alpha_1 \ldots \alpha_r$  of the polynomial $\sum c_i x^i$ of degree less than $r$.