make_mcev {mcompanion} | R Documentation |
Create a multi-companion eigenvector
Description
Creates an eigenvector of a multicompanion matrix from the eigenvalue and the seed parameters.
Usage
make_mcev(eigval, co, dim, what.co = "bottom")
make_mcgev(eigval, co, v, what.co = "bottom")
Arguments
eigval |
the eigenvalue. |
co |
the bottom (default) or the top seed elements of the vector. |
dim |
the size of the matrix. |
what.co |
type of |
v |
the previous vector in the chain. |
Details
make_mcev
computes an eigenvector for a multi-companion
dim x dim
matrix by filling its top or bottom part with
co
and completing the remaining elements using the general
pattern of eigenvectors of such matrices
(Boshnakov 2002).
Similarly, make_mcgev
computes the next generalised
eigenvector in a chain whose previous element is v
.
what.co
cannot be "top"
if the eigenvalue is
0. Generalised eigenvectors corresponding to the zero eigenvalue have
some specifics, so it is better to use the specialised functions in
that case.
Value
make_mcev
returns the required eigenvector.
make_mcgev
returns the required generalised eigenvector.
Author(s)
Georgi N. Boshnakov
References
Boshnakov GN (2002). “Multi-companion matrices.” Linear Algebra Appl., 354, 53–83. ISSN 0024-3795, doi:10.1016/S0024-3795(01)00475-X.
Examples
v1 <- make_mcev(0.5, c(1, 1), dim = 4)
v1
make_mcev(0.5, c(1, 1), dim = 4, what.co = "top")
v2 <- make_mcgev(0.5, c(0, 1), v = v1, what.co = "top")
v2
make_mcgev(0.5, c(0, 1), v = v2, what.co = "top")