- 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.
