SmallMultiCompanion-class | R Documentation |
A class for internal use for work with small multi-companion matrices.
This class is for internal use.
Objects can be created by calls of the form
new("SmallMultiCompanion", Mtop, Mbot, jdMtop, MbotXtop)
.
jdMtop
:Object of class "JordanDecomposition"
~~
Mtop
:Object of class "matrix"
~~
Mbot
:Object of class "matrix"
~~
MbotXtop
:Object of class "matrix"
~~
signature(from = "SmallMultiCompanion", to = "matrix")
: ...
signature(.Object = "SmallMultiCompanion")
: ...
signature(values = "SmallMultiCompanion", vectors = "missing")
: ...
Georgi N. Boshnakov
MultiCompanion
mat2 <- make_mcmatrix(eigval = c(1), co = cbind(c(1,1,1,1), c(0,1,0,0)), dim = 4,
len.block = c(2))
mat2
## Jordan decomp. of mat2[1:2,1:2]:
x2 <- matrix(c(1,1,-1,0), ncol =2)
jd <- matrix(c(1,0,1,1), ncol = 2)
mat2[1:2,1:2] - x2 %*% jd %*% solve(x2)
jdobj <- JordanDecomposition(values = 1, vectors = x2, heights = 2)
m1 <- new("SmallMultiCompanion", mat2[1:2, 1:2], Mbot = mat2[3:4, 1:2], jdMtop = jdobj)
m1a <- new("SmallMultiCompanion", Mbot = mat2[3:4, 1:2], jdMtop = jdobj)
as.matrix(m1) - as.matrix(m1a) # (approx.) 0's
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