• Linear Algebra

    Can I swap one matrix norm with another?

    Some matrix norms are significantly costlier than others. For example, the matrix-2 norm requires computation of eigenvalues, whereas the matrix-1 norm is simply computed by finding the column of the matrix with the largest (absolute) sum (p283 of Carl D. Meyer). Thus, the following question becomes relevant: Can we use some matrix norm in place of some other norm? Fortunately, for some applications, we can do this. First of all, for analyzing limiting behavior, it makes no difference whether we use…