A matrix norm is a mathematical concept used to measure the size or length of a matrix. It provides a way to quantify how much a matrix can stretch or shrink vectors when it acts on them. Different types of norms exist, such as the Frobenius norm and the spectral norm, each with its own method of calculation and applications. Matrix norms are essential in various fields, including numerical analysis and machine learning, as they help assess the stability and convergence of algorithms. They also play a crucial role in understanding the properties of matrices, such as their invertibility and condition number, which is vital for solving systems of equations.