They are also important because, as Cayley recognized, certain sets of matrices form algebraic systems in which many of the ordinary laws of arithmetic (e.g., the associative and distributive laws) are valid but in which other laws (e.g., the commutative law) are not valid. Cayley first applied them to the study of systems of linear equations, where they are still very useful. The term matrix was introduced by the 19th-century English mathematician James Sylvester, but it was his friend the mathematician Arthur Cayley who developed the algebraic aspect of matrices in two papers in the 1850s. Only gradually did the idea of the matrix as an algebraic entity emerge. Historically, it was not the matrix but a certain number associated with a square array of numbers called the determinant that was first recognized.
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Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics. The numbers are called the elements, or entries, of the matrix. Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. Britannica Explains In these videos, Britannica explains a variety of topics and answers frequently asked questions.
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