How to find dimension of a matrix

How to find dimension of a matrix

The matrix registers in the form of the rectangular table consisting of a number of lines and columns on which crossing matrix elements are located. The main mathematical application of matrixes – the solution of systems of the linear equations.


1. Number of columns and lines set dimension of a matrix. For example, the table dimension 5×6 has 5 lines and 6 columns. Generally, the dimension of a matrix registers in the form of m×n where number m indicates quantity of lines, n – columns.

2. It is important to consider dimension of a matrix at commission of algebraic operations. For example, it is possible to put matrixes only of the same size. Operation of addition of matrixes with different dimension is not defined.

3. If the massif has dimension of m×n, it can be increased by the n×l array. The number of columns of the first matrix has to equal to number of lines of the second, otherwise operation of multiplication will not be defined.

4. The dimension of a matrix indicates number of the equations in a system and quantity of variables. The number of lines coincides with quantity of the equations, and the variable is assigned to each column. The solution of a system of the linear equations "is written down" in actions over matrixes. Thanks to the matrix system of record becomes possible to solve the systems of high orders.

5. If the number of lines is equal to number of columns, the matrix is called square. In it it is possible to allocate the main and collateral diagonals. Main goes from the left top corner to right lower, collateral – from right top to left lower.

6. Massifs dimension of m×1 or 1×n are vectors. Also it is possible to present any line and any column of any table in the form of a vector. For such matrixes all operations over vectors are defined.

7. Having changed in a matrix A lines and columns in places, it is possible to receive the transposed matrix of A(T). Thus, when transposing the dimension of m×n will pass into n×m.

8. In programming for the rectangular table two indexes, one of which runs length of all line, another – length of all column are set. At the same time the cycle for one index is placed in a cycle for another at the expense of what consecutive passing of all dimension of a matrix is provided.

Author: «MirrorInfo» Dream Team