Home/Algebra/Matrix norms and conditioning/Matrix infinity norm24. Matrix norms and conditioningMatrix infinity normLevel: intermedioIn 24. Matrix norms and conditioningFormulaCopy LaTeX∥A∥∞=maxi∑j∣aij∣.\|A\|_\infty = \max_i\sum_j|a_{ij}|.∥A∥∞=imaxj∑∣aij∣.Tagsalgebraalgebra formulalinearnormsnorms conditioningDetailIt is the maximum absolute row sum.Explore the ideaFound an error? Contact us.Related formulasRelatedInduced matrix norm∥A∥p=maxx≠0∥Ax∥p∥x∥p.\|A\|_p = \max_{\mathbf x\neq\mathbf0} \frac{\|A\mathbf x\|_p}{\|\mathbf x\|_p}.∥A∥p=x=0max∥x∥p∥Ax∥p.Open formulaOpen in sectionRelatedMatrix 1-norm∥A∥1=maxj∑i∣aij∣.\|A\|_1 = \max_j\sum_i|a_{ij}|.∥A∥1=jmaxi∑∣aij∣.Open formulaOpen in sectionRelatedSubmultiplicativity∥AB∥≤∥A∥ ∥B∥.\|AB\| \le \|A\|\,\|B\|.∥AB∥≤∥A∥∥B∥.Open formulaOpen in section