Block Matrix Inversion

Posted on by phsamuel

Here are some formula for matrix inversion. Lemma 1: For a block matrix $latex M=\begin{pmatrix}A & B \\C &D\end{pmatrix}$, $latex M^{-1}=\begin{pmatrix}(A-B D^{-1} C)^{-1}& -A^{-1}B(D-CA^{-1}B)^{-1}\\-(D-CA^{-1}B)^{-1}CA^{-1}&(D-CA^{-1}B)^{-1}\end{pmatrix}$ $latex =\begin{pmatrix}A^{-1}+A^{-1}BS^{-1}CA^{-1}& -A^{-1}BS^{-1}\\-S^{-1}CA^{-1}&S^{-1}\end{pmatrix}$, where $latex S=D-CA^{-1}B$ is basically the Schur’s complement of block $latex A$. Proof: Let $latex M^{-1}=\begin{pmatrix}E&F\\G&H\end{pmatrix}$, $latex M M^{-1}=1$ gives us $latex AE+BG=I$ $latex AF+BH=0$ $latex CE+DG=0$ $latex…

Screen capture of a selected window with ffmpeg in Ubuntu

Posted on by phsamuel

After some trial and error and reading some other posts, I finally manage to capture screencast of a selected window with ffmpeg under 10.04. I am using the native ffmpeg from ubuntu and so recompiling is not needed. The command I’m using is as below. ffmpeg -f alsa -ac 2 -i pulse -f x11grab -r…

Code Geass Season 1

Posted on by phsamuel

What can I say? I just can’t stop watching and and basically used up my whole day to finish the first season. Thinking back, it didn’t incorporate exactly lots of new elements. After all, the studio is Sunrise. It has been making war animes for more than 30 years. It just did everything they used…

Existence of Eigenvector in Linear Operator in Complex Vector Space

Posted on by phsamuel

Here is some quick note for the existence of eigenvector for linear operator $latex T$  in complex vector space of dimension $latex n$. Consider any non-zero vector $latex X$ in the space, we have the $latex n+1$ vectors $latex X, T[X],T^2[X],T^3[X],\cdots,T^n[X]$ to be linearly dependent. Thus, there exists $latex a_0,a_1,\cdots,a_n$ such that $latex a_0+a_1T[X]+a_2T^2[X]+\cdots+a_nT^n[X]=0$. If…

America and Socialism

Posted on by phsamuel

One thing I found it amazing is how average americans detest and even are terrified by the word socialism. Sometimes I heard people will say chineses are “communists” and “socialists”. It is interesting that America is actually a much more socialistic country than China. It is true that the chinese government is dictatorship. But it…

Another look of Steins Gate

Posted on by phsamuel

I finally finished Steins Gate. Honestly, I was a little bit disappointed. It is still good, even great. But I don’t think it is a classic as some may suggest. And the quality (both visual and story-wise) definitely declines about mid way until it came back up again near the end. I guess it is…

Convert office documents and slides to pdf

Posted on by phsamuel

I was trying to show some slides in my dropbox folder to my collaborator with my android tablet. I only have the pptx file and it displays so slowly on my ASUS transformer. It came to me maybe I can connect to my desktop in office remotely to convert the slides to pdf. I did…

Over-justification Effect

Posted on by phsamuel

I am watching an online course on gamification. It mentioned explicit motivation and implicit motivation and described interesting examples of over-justification effect that subjects can be demotivated by rewards. The first one is about drawing by kids. Many kids are very interested in drawing and are inherently motivated to draw. However, when they are given…

Random Thought on Steins Gate

Posted on by phsamuel

I am more than half way through Steins Gate. Apparently, it will become one of my all time favorite. Okay, there will be spoilers here. For those who didn’t watch it, go watch it now! It doesn’t matter if you are an anime fan or not. This one will definitely change your attitude towards anime…

TF-IDF

Posted on by phsamuel

Here are some notes of TF-IDF as a measure for identifying keywords in a document. To efficiently indexing documents for future search, it is important to identify the keywords in a document. For a word $latex w$ to be a good keyword, first, it should be relatively rare. This can be measured by the inverse document frequency…