The Structure Theorem over PID’s

In this post I'll describe the structure theorem over PID's which generalizes the following results: Finite dimensional vector fields over $latex {k}&fg=000000$ are all of the form $latex {k^{\oplus n}}&fg=000000$, The classification theorem for finitely generated abelian groups, The Frobenius normal form of a matrix, The Jordan decomposition of a matrix. 1. Some ring theory… Continue reading The Structure Theorem over PID’s

Rant: Matrices Are Not Arrays of Numbers

The following is an excerpt from a current work of mine. I thought I'd share it here, as some people have told me they enjoyed it. As I'll stress repeatedly, a matrix represents a linear map between two vector spaces. Writing it in the form of an $latex {m \times n}&fg=000000$ matrix is merely a… Continue reading Rant: Matrices Are Not Arrays of Numbers