| T.matrices {matrixcalc} | R Documentation |
List of T Matrices
Description
This function constructs a list of lists. The number of components in the high level list is n. Each of the n components is also a list. Each sub-list has n components each of which is an order n square matrix.
Usage
T.matrices(n)
Arguments
n |
a positive integer value for the order of the matrices |
Details
Let {{\bf{E}}_{i,j}}\;i = 1, \ldots ,n\;;\;j = 1, \ldots ,n
be a representative order n matrix created with function E.matrices.
The order n matrix {{\bf{T}}_{i,j}} is defined as follows
{{\bf{T}}_{i,j}} = \left\{ {\begin{array}{cc}
{{{\bf{E}}_{i,j}}}&{i = j}\\
{{{\bf{E}}_{i,j}} + {{\bf{E}}_{j,i}}}&{i \ne j}
\end{array}} \right.
Value
A list of n components.
1 |
A list of |
2 |
A list of |
...
n |
A list of |
Each component j of sublist i is a matrix {\bf{T}}_{i,j}
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.
See Also
Examples
T <- T.matrices( 3 )