Hermitian.test {Matrix}R Documentation

Test a Matrix for Conjugate Symmetry

Description

Hermitian.test returns the maximum modulus of the difference between a matrix and the conjugate of its transpose. is.Hermitian checks if this value is less than a tolerance.

Usage

is.Hermitian(x, tol)
Hermitian.test(x)

Arguments

x a numeric or complex matrix.
tol tolerance for the maximum modulus of the elements of the difference elements in the lower triangle and the corresponding elements in the upper triangle.

Value

Hermitian.test returns the maximum modulus of the difference between x and its conjugate transpose. (If x is not a matrix or is not square, Inf is returned.) is.Hermitian returns a logical value according to whether the value of Hermitian.test(x) is less than or equal to the tolerance tol.

Examples

is.Hermitian(hilbert(6))  # returns TRUE
x <- Matrix(1:9,3,3)
x[row(x) > col(x)] <- t(x)[row(x) > col(x)]
is.Hermitian(x, tol = 0)  # returns TRUE
Hermitian.test(x)         # returns 0