Matrix Ranking

• Rank is a single non-negative integer number that represents the number of dimensions of information in the matrix, and is a property of the whole matrix not specifically columns or rows.
• The dimensions of information is the number of linear independent rows or columns in the matrix.
• The maximum rank is smaller or equal to the minimum of the row(m) or column(n), rank(A) <= min(m,n)

(maximum possible rank)

• Square Matrix – Full Rank m= rank A(m,m)
• Rectangle Matrix – Full Column Rank = n, when rank A(m,n) m>n
• Rectangle Matrix = Full Row Rank  =m, when rank A(m,n) m<n
• Reduced Rank,Rank Deficient = a matrix which it’s rank is less than the maximum possible rank.

• The measure of rank of a matrix is the number of linearly independent columns, which is the same thing as the number of linearly independent rows.
• So, any matrix with a rank of rowspace  will have an eqaul rank for the transpose column space.