Something like
```julia
function isApproxSymmmetric(a::Matrix{Float64})
    tmp = true
    for j in 2:size(a,1)
        for i in 1:j-1
            tmp &= abs(a[i,j] - a[j,i]) < 1e-8
        end
    end
    return tmp
end
```
is ~12 times faster on my machine.