R: Test for a skew-symmetric matrix

is.skew.symmetric.matrix {matrixcalc} | R Documentation

## Test for a skew-symmetric matrix

### Description

This function returns `TRUE` if the matrix argument x is a skew symmetric matrix, i.e., the transpose of the matrix is the negative of the matrix. Otherwise, `FALSE` is returned.

### Usage

    is.skew.symmetric.matrix(x, tol = 1e-08)

### Arguments

`x` | a numeric square matrix
`tol` | a numeric tolerance level usually left out

### Details

Let {\bf{x}} be an order n matrix. If every element of the matrix {\bf{x}} + {\bf{x'}} in absolute value is less than the given tolerance, then the matrix argument is declared to be skew symmetric.

### Value

A TRUE or FALSE value.

### Author(s)

Frederick Novomestky fnovomes@poly.edu

### References

Bellman, R. (1987). Matrix Analysis, Second edition, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics.

Horn, R. A. and C. R. Johnson (1990). Matrix Analysis, Cambridge University Press.

### Examples

    A <- diag( 1, 3 )
    is.skew.symmetric.matrix( A )
    B <- matrix( c( 0, -2, -1, -2, 0, -4, 1, 4, 0 ), nrow=3, byrow=TRUE )
    is.skew.symmetric.matrix( B )
    C <- matrix( c( 0, 2, 1, 2, 0, 4, 1, 4, 0 ), nrow=3, byrow=TRUE )
    is.skew.symmetric.matrix( C )

[Package matrixcalc version 1.0-3 Index]