The number of columns and rows specify the dimension of the matrix. For example, table dimensionu 5×6 has 5 rows and 6 columns. In the General case, the dimension of the matrix written as m×n where the number m indicates the number of rows, n – columns.
The dimension of the matrix is important to consider when performing algebraic operations. For example, it is possible to put the matrices only of the same size. The operation of addition of matrices with different dimensionYu is not defined.
If the array has the dimension m×n can be multiplied by an array of n×l. The number of columns of the first matrix must equal the number of rows of the second, otherwise the multiplication is not defined.
The dimension of the matrix indicates the number of equations in the system and the number of variables. The number of rows equals the number of equations, and each column is fixed by a variable. Solution of system of linear equations "written" in the actions on matrices. Thanks to the matrix system of recording becomes possible to solve systems of high order.
If the number of rows equal to the number of columns, the matrix is called square. It is possible to distinguish the main and the secondary diagonal. Main goes from the upper left corner to the bottom right side from the upper right to the lower left.
Arrays dimensionu m×1 or 1×n are vectors. A vector can represent any row and any column of an arbitrary table. For such matrices defined all the operations on vectors.
Changing the matrix A, rows and columns sometimes, you can get the transpose of a matrix A(T). Thus, when transposing the dimension m×n will move to n×m.
The programming for rectangular tables you specify two indexes, one of which runs the length of the whole string, the other the entire length of the column. With loop for one index inside of the loop to the other, thereby providing a consistent through the entire dimension of the matrix.