How random can you be?
Suppose I asked you to generate a random sequence of ones and zeroes. Every time you add another 1 or 0 to the sequence, I am going to predict your next choice. Do you think you can make your sequence random enough that I fail to guess more than ~50% correct? Read this post to find out. Spoiler — you are not so random.
Covariance matrix and principal component analysis — an intuitive linear algebra approach
Let's take a close look at the covariance matrix using basic (unrigorous) linear algebra and investigate the connection between its eigen-vectors and a particular rotation tranformation. We can then have fun with an interactive visualisation of principal component analysis.
Vector Transformation Visualization Tool (vtvt) — an online demo
Power iteration algorithm — a visualization
The power method is a simple iterative algorithm used to find eigenvectors of a matrix. I used vtvt to create a visualization of this algorithm.
Popularity of car colours in the Greater Toronto Area
According to a survey conducted in 2012 by PPG Industries, white (21%) and black (19%) were the two most popular colours in North America followed closely by silver and grey (16% each). Red and blue accounted for 10 and 8% respectively. I decided to test this data by taking photographs of an intersection in Mississauga, Ontario and analyzing them with the help of YOLOv3 as well as OpenCV and scikit-learn libraries.
Visualization of E, V, B fields
Most physics textbooks illustrate electric and magnetic fields with field lines which are sets of parametrized curves with tangents defined by field vectors. Field lines are great for emphasizing the directional nature of E and B fields, however they fail to convey the magnitude of forces acting on charges by such fields. One way to overcome this issue is to add level curves indicating vector magnitude.