I read this and thought “Of course norm(A) is slower than computing the sqrt of the sum of squares of the elements. norm(A) is the matrix 2-norm, which requires an SVD.”
But it isn’t! For norm(A) Julia computes the Frobenius norm, the sqrt sum of squares. Seems like a strange design choice to me, but maybe on the other handit can be counted as a case of choosing a more efficient but arguably less useful algorithm.