column space and nullspace

(1.3 hours to learn)


The column space is the subspace spanned by the columns of a matrix A. The nullspace is the set of solutions to Ax = 0. Both subspaces are useful for characterizing the sets of solutions to linear systems.


This concept has the prerequisites:


  • Know the definitions of column space and null space
  • Show that the column space and null space are subspaces
  • Show that Ax = b is solvable iff b is in the column space of A

Core resources (read/watch one of the following)


MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
Author: Gilbert Strang

Supplemental resources (the following are optional, but you may find them useful)


See also

-No Additional Notes-