JordanDecompositionDefault-class: A basic class for Jordan decompositions

In mcompanion: Objects and Methods for Multi-Companion Matrices

A basic class for Jordan decompositions

Description

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(s)

Georgi N. Boshnakov

See Also

JordanDecomposition

Examples

showClass("JordanDecompositionDefault")

m <- matrix(c(1,2,4,3), nrow = 2)
new("JordanDecompositionDefault", values = rep(0,2), vectors = m)

mcompanion documentation built on Sept. 22, 2023, 5:12 p.m.