The rank and subspace of matrices

Suppose that matrix A is a m*n matrix:

1. The number of column rank of the matrix column is rank (a), the rank of 0 space of the matrix (that is, the space composed of all the x in ax=0) is the number of the column where the free variable is located n-rank (a)

2. The line rank of the matrix equals the column rank equals rank (a), the left 0 space of the matrix (that is, the space made up of all the x in A^tx=0, T is the transpose), and the rank of M-rank (a)

Notice: Understanding subspace is a linear combination

The rank and subspace of matrices