Amatrixis a rectangular arrangement of numbers into rows and columns.•In mathematics, amatrix(plural matrices) is a rectangular array of numbers, symbols, orexpressions, arranged in rows and columns. Matrices are commonly written in boxbrackets. The horizontal and vertical lines of entries in a matrix are calledrowsandcolumns, respectively. The size of a matrix is defined by the number of rows and columnsthat it contains. A matrix withmrows andncolumns is called anm×nmatrix orm-by-nmatrix, whilemandnare called itsdimensions. The dimensions of the following matrixare2×3up(read “two by three”), because there are two rows and three columns.A= [?𝟗−?????−?]Matrix Dimensions:Each element of a matrix is often denoted by a variable with two subscripts. Forinstance,a2,1represents the element at the second row and first column of a matrix A.•The individual items (numbers, symbols or expressions) in a matrix are called itselementsorentries.Provided that they are the same size (have the same number of rows and the same number ofcolumns), two matrices can be added or subtracted element by element. The rule for matrixmultiplication, however, is that two matrices can be multiplied only when the number ofcolumns in the first equals the number of rows in the second. Any matrix can be multipliedelement-wise by a scalar from its associated field.•Matrices which have a single row are calledrow vectors, and those which have a single columnare calledcolumn vectors. A matrix which has the same number of rows and columns is called asquarematrix. In some contexts, such as computer algebra programs, it is useful to consider amatrix with no rows or no columns, called anempty matrix.
