Copyright 2012: Stuart Schaffner
This document, and the software it describes, is part of the Cairn public-source software
library. This document is the property of Stuart Schaffner, who is acting as the chief
architect for this project.
Table of Contents
1. Introduction......................................................................................................................3
2. Change of coordinates......................................................................................................4
2.1. Determining the transformation................................................................................4
3. Diagonalizing the system.................................................................................................6
3.1. Random variables in transformed coordinates..........................................................6
3.2. The diagonalized system...........................................................................................8
4. Green's functions for an eigenvalue block.......................................................................9
4.1. Single zero eigenvalue for x
i
...................................................................................10
4.2. Single nonzero eigenvalue for x
i
.............................................................................10
4.3. Complex-conjugate eigenvalue pair x
i
, x
i+1
.............................................................12
4.4. Special cases for complex-conjugate eigenvalue pairs...........................................16
4.4.1. Approximation when.......................................................................................16
4.4.2. Limit as............................................................................................................17
Draft 6 2 Printed 8/13/2021
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