r_to_n: Sizes of Matrix-based Jordan algebras

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

Description

\loadmathjax

Given the number of rows in a (matrix-based) Jordan object, return the size of the underlying associative matrix algebra

Usage

r_to_n_rsm(r)
r_to_n_chm(r)
r_to_n_qhm(r)
r_to_n_albert(r=27)
n_to_r_rsm(n)
n_to_r_chm(n)
n_to_r_qhm(n)
n_to_r_albert(n=3)

Arguments

n	Integer, underlying associative algebra being matrices of size \mjeqnn\times nn*n
r	Integer, number of rows of independent representation of a matrix-based jordan object

Details

These functions are here for consistency, and the albert ones for completeness.

For the record, they are:

• Real symmetric matrices, rsm, \mjseqnr=n(n+1)/2, \mjeqnn=(\sqrt1+4r-1)/2n=(sqrt(1+4r)-1)/2

• Complex Hermitian matrices, chm, \mjseqnr=n^2, \mjeqnn=\sqrtrn=sqrt(r)

• Quaternion Hermitian matrices, qhm, \mjseqnr=n(2n-1), \mjeqnn=\sqrt1+8r/4n=sqrt(1+8r)/4

• Albert algebras, \mjseqnr=27, \mjseqnn=3

Value

Return non-negative integers

Note

I have not been entirely consistent in my use of these functions.

Author(s)

Robin K. S. Hankin

Examples

r_to_n_qhm(nrow(rqhm()))

jordan documentation built on April 8, 2021, 5:06 p.m.