Matrix algebra is vital for quantitative psychology, statistics, and computer science. It provides a compact way to express complicated mathematical operations. A matrix M is an array of numbers organized in rows and columns. The entry Mij is the number in the ith row and jth column of M. Entries can be real or complex valued, but only real-valued matrices are considered in this entry. M may represent a data set, with participants or observations as rows and with variables as columns. This entry describes the basic operations of matrix algebra, how vectors are related to matrices, and common uses of matrix algebra.