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.
E.matrices(n)A list with \(n\) components
A sublist of \(n\) components
A sublist of \(n\) components
...
A sublist of \(n\) components
Each component \(j\) of sublist \(i\) is a matrix \({\bf{E}}_{i,j}\)
a positive integer for the order of the identity matrix
Frederick Novomestky fnovomes@poly.edu
Let \({{\bf{I}}_n} = \lbrack {\begin{array}{cccc} {{{\bf{e}}_1}}&{{{\bf{e}}_2}}& \cdots &{{{\bf{e}}_n}} \end{array}} \rbrack\) be the order \(n\) identity matrix with corresponding unit vectors \({{{\bf{e}}_i}}\) with one in its \(i\)th position and zeros elsewhere. The \(n \times n\) matrix \({{\bf{E}}_{i,j}}\) is computed from the unit vectors \({{{\bf{e}}_i}}\) and \({{{\bf{e}}_j}}\) as \({{\bf{E}}_{i,j}} = {{\bf{e}}_i}\;{{\bf{e'}}_j}\). These matrices are stored as components in a list of lists.
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.