2.68 Check if a matrix is Hermite

Problem: Given a matrix A, check to see if it is Hermite.

A Matrix is Hermite if it is the same as the conjugate of its transpose. One way to check is to take the difference and check that all values in the resulting difference matrix are zero.

To account for numerical values, the check is done using machine epsilon.

Mathematica mat = {{-1,1-3*I,0}, {1+3*I,0,-6*I}, {0,6*I,1}}; HermitianMatrixQ[mat]

True

 

Matlab clear all; i=sqrt(-1); mat=[-1 1-3*i 0; 1+3*i 0 -6*i; 0 6*i 1]; mat2=conj(transpose(mat)); diff = mat-mat2	diff = 0 0 0 0 0 0 0 0 0
r=abs(diff)<eps('double')	r = 1 1 1 1 1 1 1 1 1
all(r(:))	1

 

Maple mat := Matrix([[-1,1-3*I,0], [1+3*I,0,-6*I],[0,6*I,1]]); mat2:= LinearAlgebra:-HermitianTranspose(mat); LinearAlgebra:-Equal(mat,mat2)

true