Matrix Norm Calculator

About this calculator

A matrix norm gives a single number that measures how much a matrix can “stretch” a vector, and different norms answer that question in different ways. For a matrix induced by vector p-norms, the 1-norm equals the largest of the absolute column sums (worst-case stretch when the input is measured with the taxicab / 1-norm), while the infinity-norm equals the largest of the absolute row sums (worst-case stretch under the max-norm) — both quick to compute by hand for a small matrix, unlike the spectral (2-)norm, which needs eigenvalues.

Numerical analysts and engineers use these norms to bound error propagation in linear systems, estimate the condition number of a matrix (how sensitive a solution is to small input errors), and check convergence criteria in iterative solvers. This calculator takes the four entries of a 2×2 matrix and returns its 1-norm, infinity-norm, and largest absolute entry.