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Re: JordanDecompose[]

• To: mathgroup at smc.vnet.net
• Subject: [mg124024] Re: JordanDecompose[]
• From: danl at wolfram.com
• Date: Fri, 6 Jan 2012 04:15:19 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <je3vti$eeh$1@smc.vnet.net>
• Reply-to: comp.soft-sys.math.mathematica at googlegroups.com

Here is a mildly edited comment from the code.

"This routine uses the method based on matrix presentations.
   It is a more general method than the one used in [...]
   (the latter is faster but does not always work, for derogatory matrices).
   Initially the matrix is decomposed into subblocks, where each
   subblock has eigenvalues of the same value.  Eigenvalues in
   different subblocks are distinct.  Then elementary row and column
   operations are done on the characteristic presentations of the
   subblocks."

This was from 1993, when two of us worked on the implementation. It was based on course notes I took in 1985. (Coincidently, the class was taught by one of the original Mathematica developers, Dan Grayson.) It's been a while since bugs were spotted in that code, so I have to confess I do not remember the details.

Daniel Lichtblau
Wolfram Research