A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
Matrices are denoted with dimensions m ร n (m rows, n columns). They can be added, subtracted, and multiplied under specific rules. Key concepts include determinant, inverse, transpose, and rank. Matrices are used to solve systems of linear equations, represent transformations in computer graphics, encode data in machine learning, model networks, and describe quantum states in physics.
Matrices were developed in ancient China for solving linear equations. The term "matrix" was coined by James Joseph Sylvester in 1850. Arthur Cayley developed matrix algebra in the 1850s-1860s, defining matrix multiplication. The determinant was studied earlier by Seki Takakazu in Japan and Leibniz in Europe. Matrices became essential in 20th-century computing, physics, and data science.