id: Multiplicative identities

In jordan: A Suite of Routines for Working with Jordan Algebras

Multiplicative identities

Description

Multiplying a jordan object by the identity leaves it unchanged.

Usage

as.identity(x)
rsm_id(n,d)
chm_id(n,d)
qhm_id(n,d)
albert_id(n)
spin_id(n=3,d=5)

Arguments

n	Length of vector to be created
d	Dimensionality
x	In function as.identity(), a jordan object. Return value will be a jordan object of the same dimensionality but entries equal to the identity

Details

The identity object in the matrix-based classes (jordan_matrix) is simply the identity matrix. Function as.identity() takes an object of any of the five types (rsm, chm, qhm, spin, or albert) and returns a vector of the same length and type, but comprising identity elements.

Class spin has identity \left(1,\mathbf{0}\right).

Value

A jordan object is returned.

Author(s)

Robin K. S. Hankin

Examples

x <- as.albert(matrix(sample(1:99,81,replace=TRUE),nrow=27))
I <- as.identity(x)
x == x*I  # should be TRUE


rsm_id(6,3)

jordan documentation built on July 4, 2024, 5:06 p.m.