A basic class for Jordan decompositions

A basic class for Jordan decompositions.

Details

Class "JordanDecompositionDefault" represents Jordan decompositions. It inherits from the virtual class "JordanDecomposition", which serves as a base class for Jordan decompositions. These classes should be considered internal.

Objects from the Class

Objects from class "JordanDecompositionDefault" can be created by a call to JordanDecomposition().

Objects can be created by calls of the form new("JordanDecompositionDefault", heights, ...).

Slots

values:: Object of class "number", vector of eigenvalues (one value for each Jordan chain).
heights:: Object of class "integer", the heights of the Jordan chains.
vectors:: Object of class "matrix", the (generalised) eigenvectors (similarity matrix).

Extends

Class "JordanDecomposition", directly.

Methods

coerce

signature(from = "JordanDecompositionDefault", to = "matrix"):

gives the matrix represented by the Jordan decomposition, i.e. \(XJX^{-1}\). As with other coerce methods, use as(obj, "matrix"), where obj is the Jordan decomposition object.

initialize

signature(.Object = "JordanDecompositionDefault"): ...

Author

Georgi N. Boshnakov

Examples

showClass("JordanDecompositionDefault")
#> Class "JordanDecompositionDefault" [package "mcompanion"]
#> 
#> Slots:
#>                               
#> Name:   values heights vectors
#> Class:  number integer  matrix
#> 
#> Extends: "JordanDecomposition"

m <- matrix(c(1,2,4,3), nrow = 2)
new("JordanDecompositionDefault", values = rep(0,2), vectors = m)
#> An object of class "JordanDecompositionDefault"
#> Slot "values":
#> [1] 0 0
#> 
#> Slot "heights":
#> [1] 1 1
#> 
#> Slot "vectors":
#>      [,1] [,2]
#> [1,]    1    4
#> [2,]    2    3
#>