Matrix Norms and their Sensitivity to Noise a Computational Study

Most of the objective (cost) functions in op-timization techniques utilize norms especially when dealing with signals, vectors, or matri-ces. In this work, three norms were studied, namely matrix One norm, Infinity norm, and Frobenius (Euclidean or Two) norm. The ef-fect of noise on these matrix norms was stud-ied with the aid of a generalized eigen equa-tion. Basic analysis of the effect of noise on matrix norms is provided, which is also com-plimented with a computer simulated results. It turns out that the Frobenius norm is the least sensitive norm to noise