Rank and mullity
Rank and nullity measure the dimensions of key subspaces associated with a matrix. The rank is the dimension of the column space (or row space), while the nullity is the dimension of the null space. These are connected by the rank-nullity theorem: $\text{rank}(A) + \text{nullity}(A) = n$ for an $m \times n$ matrix.
Parents
Children
- Definition of column rank of a matrix
- Definition of rank of a matrix
- Definition of nullity of a matrix
- The rank of a matrix equals number of pivots in a reduced row echelon form.
- The rank of a matrix equals the rank of the linear transformation it represents.
- The row space and the column space of a matrix have the same dimension.
- If A is a matrix