reduce_chains_simple: Transform a chain and drop excess, internal function

In mcompanion: Objects and Methods for Multi-Companion Matrices

Transform a chain and drop excess, internal function

Description

Transform a chain and drop excess, internal function.

Usage

reduce_chains_simple(chains, sort = TRUE)

Arguments

chains	list of 0chains
sort	flag for sorting, see details

Details

Given one or more chains corresponding to a common eigenvalue, reduce_chains_simple transforms the chains so that redundant eigenvectors are removed. In the process, the heights of some chains may decrease and the number of chains may be reduced, too.

If sort == TRUE the function reorders the chains so that their lengths are in decreasing order. However, the algorithm depends on this being done, so this argument should be used when the chains are known to be already sorted.

I wrote this function as part of the support for chains of multi-companion matrices associated with the 0 eigenvalue. When chains specified via the top left mo.col x mo.col subchains are extended to chains of the top left mo x mo corner the (extended) eigenvectors may not be linearly independent.

Value

list of chains

Author(s)

Georgi N. Boshnakov

See Also

mc.0chain.dx

mcompanion documentation built on Sept. 22, 2023, 5:12 p.m.