For elliptic curves, it's easier to prove that addition is commutative than to prove it is associative.

Dr. Gilbert Strang and Lex Fridman discuss the theory behind singular value decomposition (SVD), which is a very important concept in machine learning.

A regular n-gon is constructible by straightedge and compass iff φ(n) is a power of 2. φ = Euler's totient function.

Let R be an integral domain. Then R is a field iff every finitely generated R-module is free.

What is algebraic geometry?

youtu.be/MflpyJwhMhQ?fe…

Encryption in groups of unknown order johndcook.com/blog/2021/08/2…

'Generalisations of a structure can look very different depending on which particular description of it we started with.' -- Eugenia Cheng

Schur Decomposition: Every square matrix A can be factored as A = QUQ^{-1} where Q is unitary and U is upper triangular.

'Lie algebras behave simpler than groups but not as simple as numbers.' -- Terry Gannon

Trig mnemonic diagrams
johndcook.com/blog/trig-mnem…

First exponential sum of May

johndcook.com/expsum/?y=24&m…

New post: Applied abstraction

johndcook.com/blog/2024/05/0…

A matrix M is normal <=> M* M = M M* <=> M = U D U* where U is unitary and D diagonal.

Sure, you've heard of verifying trig identities... but what about verifying 'log identities'?

Why don't we do this?

Perfect codes johndcook.com/blog/2020/02/2…

A real matrix has orthogonal eigenvectors if and only if it commutes with its transpose.

How Albrecht Dürer drew an 11-sided figure

johndcook.com/blog/2023/04/1…

A semi-ring generalizes the definition of a ring by dropping the requirement that elements have additive inverses. e.g. non-negative reals