E.matrices {matrixcalc} | R Documentation |
List of E Matrices
Description
This function constructs and returns a list of lists. The component of each sublist is a square matrix derived from the column vectors of an order n identity matrix.
Usage
E.matrices(n)
Arguments
n |
a positive integer for the order of the identity matrix |
Details
Let be the order
identity matrix
with corresponding unit vectors
with one in
its
th position and zeros elsewhere.
The
matrix
is computed
from the unit vectors
and
as
. These matrices
are stored as components in a list of lists.
Value
A list with components
1 |
A sublist of |
2 |
A sublist of |
...
n |
A sublist of |
Each component of sublist
is a matrix
Note
The argument n must be an integer value greater than or equal to 2.
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications, SIAM Journal on Algebraic Discrete Methods, 1(4), December 1980, 422-449.
Magnus, J. R. and H. Neudecker (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics, Second Edition, John Wiley.
Examples
E <- E.matrices( 3 )