Matrix Norms

Matrix norms are mathematical tools that measure the size or "magnitude" of a matrix, similar to how we measure length or volume. They help quantify how large the numbers in a matrix are, or how much the matrix can stretch or amplify a vector when multiplied. Different norms serve different purposes; some focus on the largest effect the matrix can have, while others consider the overall sum of entries. Matrix norms are essential in numerical analysis, stability analysis, and optimization, providing a way to assess and control the behavior of matrix operations in various applications.