There are several applications of matrices in multiple branches of science and different mathematical disciplines. Most of them utilize the compact representation of a set of numbers within a matrix.

Data that can be organized in rows and columns can be represented as a matrix. In computer science, matrices are used in the projection of three dimensional images into two dimensional screens. Scholastic matrices are used by page rank algorithms. Cryptography is also implemented using matrices.

In physics, matrices are applied in optics, quantum mechanics and electrical circuits. Matrices can also be used to represent real-world data like the traits or habits of a population. Matrices are also applied in economics to study stock market trends and to optimize profit and minimize loss, in chemistry to find quantities in a chemical solution, and in genetics to work out the selection process.