duplication.inverse {rggm}R Documentation

The inverse of a duplication matrix

Description

Return the inverse of a duplication matrix, so called an elimination matrix

Usage

duplication.inverse(n)
elimination(n)

Arguments

n a positive integer, indicating a dimmension

Value

An n*(n+1)/2 rows n columns elimination matrix.

Author(s)

Masashi Miyamura

References

Jan R. Magnus and Heinz Neudecker, (1999) Matrix Differential Calculus with Applications in Statistics and Econometrics, Second Edition, John Wiley & Sons

See Also

vech, duplication, elimination

Examples

  m <- matrix(c(1, 2, 3,
                2, 5, 6,
                3, 6, 9),
              3, 3)
  elimination(3) %*% as.vector(m) # identical to vech(m)

  duplication.inverse(3) %*% duplication(3) # An identity matrix
  elimination(3) %*% duplication(3) # The same thing

[Package rggm version 1.0.1 Index]