The Helmert sub-matrix {Compositional}

The Helmert sub-matrix

Description

The Helmert sub-matrix.

Usage

helm(n)

Arguments

n

A number grater than or equal to 2.

Details

The Helmert sub-matrix is returned. It is an orthogonal matrix without the first row.

Value

A (n-1) \times n matrix.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail] and Giorgos Athineou <[e-mail]>.

References

Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. https://arxiv.org/pdf/1106.1451.pdf

John Aitchison (2003). The Statistical Analysis of Compositional Data, p. 99. Blackburn Press.

Lancaster H. O. (1965). The Helmert matrices. The American Mathematical Monthly 72(1): 4-12.

See Also

alfa, alfainv

Examples

helm(3)
helm(5)