| coerce {jordan} | R Documentation |
Coercion
Description
Various coercions needed in the package
Usage
as.jordan(x,class)
vec_to_rsm1(x)
vec_to_chm1(x)
vec_to_qhm1(x)
vec_to_albert1(x)
rsm1_to_vec(M)
chm1_to_vec(M)
qhm1_to_vec(M)
albert1_to_vec(H)
as.real_symmetric_matrix(x,d,single=FALSE)
as.complex_herm_matrix(x,d,single=FALSE)
as.quaternion_herm_matrix(x,d,single=FALSE)
as.albert(x,single=FALSE)
numeric_to_real_symmetric_matrix(x,d)
numeric_to_complex_herm_matrix(x,d)
numeric_to_quaternion_herm_matrix(x,d)
numeric_to_albert(e1)
as.list(x,...)
matrix1_to_jordan(x)
Arguments
x, e1 |
Numeric vector of independent entries |
M, H |
A matrix |
d |
Dimensionality of algebra |
single |
Boolean, indicating whether a single value is to be returned |
class |
Class of object |
... |
Further arguments, currently ignored |
Details
The numeral “1” in a function name means that it operates on,
or returns, a single element, usually a matrix. Thus function
as.1matrix() is used to convert a jordan object to a list of
matrices. Length one jordan objects are converted to a matrix.
Functions vec_to_rsm1() et seq convert a numeric vector to a
(symmetric, complex, quaternion, octonion) matrix, that is, elements
of a matrix-based Jordan algebra.
Functions rsm1_to_vec() convert a (symmetric, complex,
quaternion, octonion) matrix to a numeric vector of independent
components. The upper triangular components are used; no checking for
symmetry is performed (the lower triangular components, and non-real
components of the diagonal, are discarded).
Functions as.real_symmetric_matrix(),
as.complex_herm_matrix(), as.quaternion_herm_matrix()
and as.albert() take a numeric matrix and return a
(matrix-based) Jordan object.
Functions numeric_to_real_symmetric_matrix() have not been
coded up yet.
Function matrix1_to_jordan() takes a matrix and returns a
length-1 (matrix based) Jordan vector. It uses the class of the
entries (real, complex, quaternion, octonion) to decide which type of
Jordan to return.
Value
Return a coerced value.
Author(s)
Robin K. S. Hankin
Examples
vec_to_chm1(1:16) # Hermitian matrix
as.1matrix(rchm())
as.complex_herm_matrix(matrix(runif(75),ncol=3))
matrix1_to_jordan(cprod(matrix(rnorm(35),7,5)))
matrix1_to_jordan(matrix(c(1,1+1i,1-1i,3),2,2))
matrix1_to_jordan(Oil + matrix(1,3,3))