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Table of Contents Math Background Matrices Rank of a Matrix  
See also: matrix determinant, order of a matrix, linear dependence 
The order of a matrix is a measure of its shape and size. However, the order does not provide any hints on the information content of a matrix. The 53matrices



differ in their information content, since the first and the second matrix contain rows and columns which are multiples of other rows and columns (some rows/columns are linearly dependent). The concept of linear independence leads to the definition of the row and column rank of an arbitrary matrix A:
Row Rank Column Rank 
The maximum number of linearly independent rows in A is called the row rank of A; the maximum number of linearly independent columns in A is called the column rank of A. 
It is a very important, and somewhat even surprising, result of matrix
theory that row and column rank of a given matrix are always equal, no
matter how the matrix is shaped. Thus, we don't have to distinguish between
row and column rank of a matrix  we simply speak of the rank of a
matrix.
Last Update: 2005Jän25