- A Measure Theory Surprise
The class of Borel sets in the Euclidean space is not closed under linear transformation.
- The spectral theorem and the singular value decomposition
Turning a matrix into a diagonal matrix simplifies many problems and thus is of particular interest. We take a look at the spectral theorem, which captures the diagonalizability of self-adjoint operators, and the singular value decomposition, which generalizes it to non-square matrices.
- Deriving Dynkin’s theorem from the monotone class theorem
Dynkin’s theorem is an extensively applicable result in measure theory. Here, we prove the theorem in a more roundabout way, using the monotone class theorem.
- Quick way to emulate a database in Rust
How I emulate a key-value store in Rust using a quick and dirty way.
- Interactive notes on finite-state machine
As I am self-studying theory of computation, specifically the theory of finite automata right now, I am making some notes on the topic to better reinforce what I have learnt, with interactive demonstrations of the automata.
- Discontinuities of a real function
What can we say about the set of discontinuities of a function on the real line?
- On the importance of trusting trust
Are supply chain attacks justifiable by the explicit no warranty clause in open source licenses?