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

peterlam · Jul 25, 2011

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 · Jul 25, 2011

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

micromass · Jul 25, 2011

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.

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

Discussion

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

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