Chapter 7
Other Canonical Forms
Roger A. Horn
The University of Utah
Vladimir V. Sergeichuk
Institute of Mathematics, Ukraine
We discuss canonical forms for several equivalence relations other than similarity. See Chapter 6 for information about canonical forms for the equivalence relation of similarity, and see the introduction to Chapter 6 for a discussion of the concept of a canonical form for an equivalence relation on ℂm × n.
7.1 Equivalence and Unitary Equivalence
Definitions:
Matrices A, B ∈ ℂm × n are equivalent if there are nonsingular matrices S ∈ ℂm × m and T ∈ ℂn × n such that A = SBT; they are unitarily equivalent if there are unitary matrices V ∈ ℂm × m and W ∈ ℂn×n such that A = VBW.
Facts:
See [HJ13, Chaps. 0 and 2] for the following ...
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