JordanDecomposition | R Documentation |
Create objects representing Jordan decompositions.
JordanDecomposition(values, vectors, heights, ...)
values |
eigenvalues, a vector of length equal to the number of Jordan chains. |
vectors |
the (generalised) eigenvectors, a matrix. |
heights |
a vector of positive integers, |
... |
further arguments that may be needed by methods. |
JordanDecomposition
is an S4 generic function. It creates
objects representing Jordan decompositions. Dispatch is on the first
two arguments, values
and vectors
.
The names of the arguments correspond to slots in class "JordanDecompositionDefault", which is the class of the objects created by methods in package mcompanion and inherits from the virtual class "JordanDecomposition".
an object inheriting from "JordanDecomposition"
signature(values = "ANY", vectors = "ANY")
the default method; currently raises an error.
signature(values = "JordanDecomposition", vectors = "missing")
simply returns values
.
signature(values = "list", vectors = "missing")
In this case values
can be a list with components "values"
,
"vectors"
and "heights"
. This method has an additional
argument "names"
which can be used when the components of the
list are different, e.g.
names = c(values = "eigval", vectors = "eigvec", heights = "len.block")
.
signature(values = "missing", vectors = "matrix")
This is equivalent to the case values = "number"
with values
set to a vector of missing values.
signature(values = "missing", vectors = "missing")
values
(vectors
) is set to a vector (matrix) of missing
values. The dimensions are deduced from argument heights
, so
heights
cannot be missing for this signature.
signature(values = "number", vectors = "matrix")
This is equivalent to calling new
for class
"JordanDecompositionDefault"
with arguments values
,
vectors
and heights
.
signature(values = "number", vectors = "missing")
This is equivalent to the case vectors = "matrix"
with vectors
set to a matrix of missing values.
signature(values = "SmallMultiCompanion", vectors = "missing")
This computes the Jordan decomposition of an object from class "SmallMultiCompanion".
Georgi N. Boshnakov
m <- matrix(c(1,2,4,10), nrow = 2)
m <- matrix(c(1,2,4,10), nrow = 2)
m <- matrix(c(5, 12, 3, 4), nrow = 2)
JordanDecomposition(values = rep(0,2), vectors = m)
jd <- JordanDecomposition(values = c(0.9, 0.3), vectors = m)
as(jd, "matrix")
eigen(jd)
## the eigenvectors are scaled versions of m's columns:
eigen(jd)$vectors %*% diag(c(5 / eigen(jd)$vectors[1,1], -5))
## == m
## eigenvalues are not supplied, so set to NA's here:
JordanDecomposition(vectors = m)
## eigenvectors are set to vectors of NA's here:
JordanDecomposition(values = rep(0,2), height = c(1,1))
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