March 5, 2020

eigenvalue decomposition of Pauli matrices

At the heart of linear algebra is a task called eigenvalue decomposition. This task, in the simplest words possible, allows you to analyze a given matrix to determine how it’s constructed from a combination of basis vectors, called eigenvectors, and scalars, called eigenvalues. Many statistical models, machine learning algorithms, and scientific theories use eigenvector decomposition to go from a muddle of data to a understandable theory. Here, I’ll talk about using eigenvalue decomposition to inspect the fundamental logic gates used in quantum computing. Read more

December 25, 2019

mathematical tools

When performing some job, I may need to use certain tools: a scrub for cleaning the bathroom; a knife for cutting vegetables; a hand drill for securing a shelf; etc. Let’s suppose the job concerns problem-solving. I may reach for a high level mental model appropriate for the problem. When we arrive at a specialty problem, like in a field of mathematics, the tools become more specialized too. I’m currently participating in Machine Learning Tokyo’s もくもく reading group, discussing the textbook Mathematics for Machine Learning; the mathematical field of interest is linear algebra. Here are the tools I see that one needs to learn in order to complete exercises at the end of each chapter of the book: Read more

August 19, 2019

leonardo's recurrance

I have finished reading An Imaginary Tale by Paul Nahin. About three quarters of the way through the book, I started fiddling with an example of applied complex analysis: representing a particular family of recurrence relations as an equation in complex numbers. I learned quite a bit along the way, and I even wrote some toy code to try out the efficiency of the approach. Read more

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