Matrix Canonical Forms

TL;DR

This paper provides an educational overview of matrix canonical forms, emphasizing linear algebra fundamentals and proof techniques for graduate students in combinatorics.

Contribution

It offers a detailed, pedagogical presentation of matrix canonical forms aimed at developing proof and notation skills for graduate students.

Findings

Comprehensive review of linear algebra essentials.

Development of general matrix canonical forms.

Educational focus for graduate-level learning.

Abstract

This material is a rewriting and expansion of notes for beginning graduate students in seminars in combinatorics (Department of Mathematics, University of California San Diego). Solid skills in linear and multilinear algebra were required for these seminars. We focused on a review of linear algebra and a careful development of the general matrix canonical forms as a training ground for the necessary proof and notational skills.