Test for Symmetry or Conjugate Symmetry in a Matrix
DESCRIPTION:
Either tests whether or not a Matrix is real symmetric or complex Hermitian,
or else gives a metric by which such a test can be made.
.LB Matrix
USAGE:
is.Hermitian(x, tol)
Hermitian.test(x)
REQUIRED ARGUMENTS:
- x
-
an numeric or complex matrix.
OPTIONAL ARGUMENTS:
- tol
-
tolerance for the maximum modulus for the difference between elements in the
lower triangle and the corresponding elements in the upper triangle.
VALUE:
For
is.Hermitian
, a logical value is returned.
If
tol
is missing, this value is equivalent to
inherits(x, "Hermitian")
.
Otherwise the result is
TRUE
if the maximum modulus for the difference
between elements in the lower triangle and the corresponding elements in the
upper triangle is less than or equal to
tol
, and
FALSE
otherwise.
For
Hermitian.test
, the maximum modulus for the difference between elements
in the lower triangle and the corresponding elements in the upper triangle is
returned.
EXAMPLES:
x <- Matrix(1:9,3,3)
x[row(x) > col(x)] <- t(x)[row(x) > col(x)]
is.Hermitian(x)
# [1] F
is.Hermitian(x, tol = 0)
# [1] T
Hermitian.test(x)
# [1] 0