The matrix is the mathematical object representing the rectangular table. On crossing of columns and lines of this table matrix elements – the whole, real or complex numbers are located. The size of a matrix is established by quantity of its lines and columns. Types of matrixes and action over them are studied in matrix algebra.
Rules of mathematical operations with matrixes allow to apply them to record of systems of the equations widely. At the same time in lines of a matrix the equations, and in columns – unknown register. Thus, the solution of a system of the equations svoiditsya to performance of operations with a matrix.
Matrixes can be put and subtracted provided that all composed matrixes have the same size. Besides, they can be multiplied in several ways. The first way – multiplication of a matrix with a certain quantity of columns on the right on a matrix with the same quantity of lines. The second way – multiplication by a vector matrix provided that this vector is considered as a separate case of a matrix. The third way – multiplication of a matrix by scalar size.
For the first time matrixes began to apply mathematicians of Ancient China to the solution of the linear equations. Along with them also the Arab mathematicians who developed for them the principles and rules of addition began to use matrixes. However the term "matrix" was entered only in 1850. Before they were called "magic squares". Matrixes are designated by capital letters And: MxN, where And – a name of a matrix, M– quantity of lines in a matrix, and N– quantity of columns. Elements – the corresponding lowercase letters with the indexes designating their number in line and in column a (m, n). squared matrixes are often widespread though far back in the past mathematicians considered also triangular. If the quantity of lines and columns of a matrix equally, it is called square. At this M=N already has the name of an order of a matrix. The matrix having only one line is called as line. The matrix with only one column is called a column. The diagonal matrix is a square matrix in which only the elements located on diagonal are not equal to zero. If all elements are equal to unit, the matrix is called single if to zero – zero. If in a matrix to trade places of a line also columns, it will become transposed. If to replace all elements complex interfaced, it will become complex interfaced. Besides, there are also other types of matrixes which are defined by conditions which are imposed on matrix elements. But the majority of such conditions is applicable only to square matrixes.