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 1.0-6 Index]