Blog
Recent Posts
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On Acyclic Models
We “discover” a generalization to the Fundamental Theorem of Homological Algebra (or Comparison Theorem) that is used in many a proof in algebraic topology; the Acyclic Models Theorem.
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Waveguide Mode Orthogonality is an Eigenvalue Problem
We provide a short exposition on the connections between mode orthogonality in waveguides/resonators and the spectrum of linear operators in the context of electromagnetic theory.
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Direct Derivation of Rotation Matrix
A first-principles approach to rotation in $\mathbb{R}^3$ given an orthogonal matrix with $\det A = 1$.
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Interesting Property of Binomial Distributions
Observing the behavior of $B(n, p)$ for $np \in \mathbb{Z}$.