Matrix

A rectangular array of numbers or other entries, together with the rules of arithmetic that combine such arrays. James Joseph Sylvester coined the word matrix in 1850, in a paper titled A New Class of Theorems, describing it as an oblong arrangement of terms out of which various determinants can be produced from the square arrays it contains. Arthur Cayley gave the concept its formal algebra in A Memoir on the Theory of Matrices, read to the Royal Society in January 1858, defining matrix addition, multiplication, scalar multiplication and inverses, and demonstrating for two-by-two matrices what is now called the Cayley-Hamilton theorem. The underlying practice of solving systems of linear equations by systematic elimination is far older still, appearing in the Chinese text Nine Chapters on the Mathematical Art around 200 BC, and Carl Friedrich Gauss used the method methodically, arranging coefficients much as a matrix would, while computing the orbit of the asteroid Pallas between 1803 and 1809, decades before the matrix itself was named. John von Neumann later put matrices to work representing the payoffs of a game in Theory of Games and Economic Behavior, written with Oskar Morgenstern in 1944.