matrix mechanics: see quantum theory.

matrix, in mathematics, a rectangular array of elements (e.g., numbers) considered as a single entity. A matrix is distinguished by the number of rows and columns it contains. The matrixis a 2×3 (read "2 by 3") matrix, because it contains 2 rows and 3 columns. A matrix having the same number of rows as columns is called a square matrix. The matrixis a 2×2 matrix, or square matrix of order 2; a square matrix of order n contains n rows and n columns. Definitions are made for certain operations with matrices; for example, a matrix may be multiplied by a number, and two matrices of the same order may be added or multiplied using an algebra of matrices that has been developed. Matrices find application in such fields as vector analysis and the solution of systems of linear equations by means of electronic computers.

Set of numbers arranged in rows and columns to form a rectangular array. Matrix elements may also be differential operators, vectors, or functions. Matrices have wide applications in engineering, physics, economics, and statistics, as well as in various branches of mathematics. They are usually first encountered in the study of systems of equations represented by matrix equations of the form math.Amath.x = math.B, which may be solved by finding the inverse of matrix math.A or by using an algebraic method based on its determinant.

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