matrixcalc (version 1.0-3)

T.matrices: 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

Value

A list of \(n\) components.

1

A list of \(n\) components

2

A list of \(n\) components

...

n

A list of \(n\) components

Each component j of sublist i is a matrix {\bf{T}}_{i,j}

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 \({{\bf{T}}_{i,j}} = \left\{ {\begin{array}{*{20}{c}} {{{\bf{E}}_{i,j}}}&{i = j}\\ {{{\bf{E}}_{i,j}} + {{\bf{E}}_{j,i}}}&{i \ne j} \end{array}} \right.\)

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

E.matrices

Examples

# NOT RUN {
T <- T.matrices( 3 )
# }