In matrix decomposition, the process of breaking down a matrix into a product of simpler matrices is known as _____ decomposition.

The process of breaking a matrix down into a product of simpler matrices is called **factorization** decomposition. Factorization means expressing the original matrix as a product of matrices that are easier to work with, such as diagonal, triangular, or orthogonal matrices. For example, a 2×2 matrix can be factored into a lower‑triangular matrix times an upper‑triangular matrix in LU factorization. This makes solving linear systems or computing determinants simpler. The key idea is that the product of the factor matrices exactly reproduces the original matrix.