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.
T.matrices(n)A list of \(n\) components.
A list of \(n\) components
A list of \(n\) components
...
A list of \(n\) components
Each component \(j\) of sublist \(i\) is a matrix \({\bf{T}}_{i,j}\)
a positive integer value for the order of the matrices
Frederick Novomestky fnovomes@poly.edu
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
\({{\bf{T}}_{i,j}} = \left\{ {\begin{array}{cc}
{{{\bf{E}}_{i,j}}}&{i = j}\\
{{{\bf{E}}_{i,j}} + {{\bf{E}}_{j,i}}}&{i \ne j}
\end{array}} \right.\)
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.
E.matrices