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…
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…
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…
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…
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…
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…
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…
I am studying an online class on Web Intelligence and Big Data. Dr. Shroff described a very nice example of LSH. Below are some quick notes. The idea of LSH is essentially the same as dimension reduction. We have some data vector $latex x$ that can be in very high dimension. By processing hash data…
Here is some personal notes on Bernstein-Vazirani algorithm. Assume that we have a black box that does nothing but compute $latex u \cdot x$, where $latex x$ is an input binary vector and $latex u$ is another binary vector that we don’t know its value. Note that all operation is bit-wise and so the output…
The effect of applying Hadamard gates to multiple qubits is rather subtle and is used in many quantum algorithms. Consider $latex n$ input qubits, $latex |u_1 u_2 u_3 \cdots u_n\rangle$. What will be the output if we apply the Hadamard gate to each of the qubit? Note that a Hadamard gate maps $latex |0\rangle$ to…