Matrix rank

The rank of a matrix is the highest order of its non-zero minor, denoted by Rank(A), Rang(A) or Rg(A). The term rank of a matrix is closely related to both its minor and determinant. This is an important characteristic used in calculating systems of linear equations.

The rank is used, in particular, to determine the compatibility of a system, i.e., the possibility of its solution in principle. In mathematics, three main methods are used to find the rank of a matrix. These are the method of enclosing minors, the method of minor enumeration, and the Gauss method, which involves performing elementary transformations on the matrix being studied.

Elementary transformations occur when rearranging rows or columns, multiplying them by a non-zero number k, when summing the elements of a row or column with the elements of another row or column of the matrix, which are multiplied by a non-zero number k.