If I copied your matrix correctly:
julia> a3 = [0 sqrt(2)/2 sqrt(2) sqrt(2)/2 0 -sqrt(2)/2 -sqrt(2) -sqrt(2)/2;
-sqrt(2)/2 -sqrt(2) 0 sqrt(2)/2 sqrt(2) -sqrt(2)/2 0 -sqrt(2)/2]
2×8 Matrix{Float64}:
0.0 0.707107 1.41421 0.707107 0.0 -0.707107 -1.41421 -0.707107
-0.707107 -1.41421 0.0 0.707107 1.41421 -0.707107 0.0 -0.707107
julia> norm(a3)
3.464101615137755
the result looks correct to me: the sum of the squares of the elements is 12, it’s square root is 3.464…, which is the 2-norm. Does Matlab give the 2-norm as well with the norm
function?