# E.matrices: List of E Matrices In matrixcalc: Collection of functions for matrix calculations

## 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

 1 E.matrices(n) 

## Arguments

 n a positive integer for the order of the identity matrix

## Details

Let {{\bf{I}}_n} = ≤ft[ {\begin{array}{*{20}{c}} {{{\bf{e}}_1}}&{{{\bf{e}}_2}}& \cdots &{{{\bf{e}}_n}} \end{array}} \right] be the order n identity matrix with corresponding unit vectors {{{\bf{e}}_i}} with one in its ith 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.

## Value

A list with n components

 1  A sublist of n components 2  A sublist of n components

...

 n  A sublist of n components

Each component j of sublist i is a matrix {\bf{E}}_{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.

## Examples

 1 E <- E.matrices( 3 ) 

### Example output




matrixcalc documentation built on May 2, 2019, 1:45 p.m.