If a matrix has nullity 1, what spans its null space?

[peterlam]

For a matrix A, if its nullity is equal to 1, what is the implication of that? What spans its null space?

Thanks a lot!

 

[pmsrw3]

The null space of a nullity 1 matrix is spanned by a single vector. What that vector is depends on the matrix.

 

[micromass]

Some easy implications are that the matrix will not be invertible. Moreover, A will have 0 has an eigenvalue and the geometric multiplicty of 0 will be 1.