matrixcalc (version 1.0-6)

N.matrix: Construct N Matrix

Description

This function returns the order n square matrix that is the sum of an implicit commutation matrix and the order n identity matrix quantity divided by two

Usage

N.matrix(n)

Value

An order \(n\) matrix.

Arguments

n

A positive integer matrix order

Author

Frederick Novomestky

Details

Let \({\bf{K}_n}\) be the order \(n\) implicit commutation matrix (i.e., \({{\bf{K}}_{n,n}}\) ). and \({{\bf{I}}_n}\) the order \(n\) identity matrix. The formula for the matrix is \({\bf{N}} = \frac{1}{2}\left( {{{\bf{K}}_n} + {{\bf{I}}_n}} \right)\).

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

K.matrix

Examples

N <- N.matrix( 3 )
print( N )