Extend multi-companion eigenvectors(non0)

Extend eigenchains corresponding to non-zero eigenvalues of a multi-companion matrix to higher dimension.

Usage

mC.non0chain.extend(ev, newdim)

Arguments

ev

eigenvalues and eigenvectors, a list with components ??? (as in mc_chain_subset, etc)

newdim

the new dimension of the vectors

Details

The eigenvectors of a multi-companion matrix have a special structure. This function extends the supplied eigenvectors to be eigenvectors of a higher-dimensional multi-companion matrix of the same multi-companion order with the same top rows extended with zeroes.

The function handles also the case when only the first mo.col columns of the top of the original multi-companion matrix are non-zero. This may be specified by a component mo.col in ev (otherwise mo.col is set to the number of eigenvalues).

A component len.block of ev may be used to specify lengths of the Jordan chains, the default is 1.

When mo.col is smaller than the multi-companion order, the information in the eigenvectors is not sufficient to extend them. The missing entries must be supplied via the argument x0.

Value

The eigenvectors extended to the new dimension.

Author

Georgi N. Boshnakov

Note

This is mostly internal function. The user function is mc_chain_extend.

See also

mc_chain_extend