Matrix Norm

A matrix norm is a way to measure the size or magnitude of a matrix, similar to how a length measures the size of a line segment. It assigns a non-negative number that indicates how "big" or "strong" the matrix is, reflecting how much it can stretch or amplify a vector it multiplies. Different norms provide different perspectives—for example, some focus on the largest effect on a single vector, while others consider overall energy or size. Matrix norms are essential in analyzing the stability, convergence, and sensitivity of systems involving matrices.