Chapter 6

Canonical Forms for Similarity

Leslie Hogben

Iowa State University and American Institute of Mathematics

Intuitively, a canonical form is a representative of an equivalence class that has a particularly simple form (or a form well suited to a specific purpose). More precisely, let S be a given set (e.g., of matrices), and let ~ be an equivalence relation on S (e.g., similarity). For any aS, let Sa = {bS : b ~ a} denote the equivalence class that contains a. Then ∪a∈SSa = S and for each a, bS, either Sa = Sb (if a ~ b) or SaSb = Ø (if ab). Let the set CS be a distinguished set of elements of S, one from each equivalence class, i.e., ∪a∈CSa = S and SaSb = Ø whenever a, bC and ab. For a given aS, cC is ...

Get Handbook of Linear Algebra, 2nd Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.