Re: JordanDecompose[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg124125] Re: JordanDecompose[]*From*: danl at wolfram.com*Date*: Tue, 10 Jan 2012 05:57:55 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <je3vti$eeh$1@smc.vnet.net> <je6e5h$q7b$1@smc.vnet.net> <jee7pc$cjq$1@smc.vnet.net>*Reply-to*: comp.soft-sys.math.mathematica at googlegroups.com

I should have made that clear. The [...] referred by name to a function in the code, not a reference from the literature. I did not want to put internal function names in my post. That function handles the case where the matrix is nonderogatory. More specifically, it handles all eigenvalues that have geometric multiplicity of 1 (I think it also handles the simple case where gemoetric multiplicity = algebraic multiplicity). The algorithm is not a proprietary secret. I simply cannot find a reference in the literature that seems to describe it. All I have is old lecture notes, if indeed I still have those. There is something slightly similar, I think, in the text Linear Algebra by Charles Curtis. Itworks out the rational canonical form, then notes that this gives the Jordan decomposition in the special case where we work over the algebraic closure of the matrix coefficients field. Also I think there may be something similar in the algebra text by Dummit and Foote. Daniel Lichtblau Wolfram Research