Subspace

Column spaces can contain matrices, vectors, or complex numbers. A vector space $R^n$ contains the full set of vectors with $n$ components. If there exists a set $S$ containing its own set of $n$-dimensional vectors, but it doesn’t span the entire $R^n$ space, it is a subspace.

Rules for Subspaces

• All linear combinations of objects in a subspace also lie in that subspace
• Every subspace must contain the zero-space $Z=0$

Subspaces

• Column Space
• Left Null Space
• Row Space
• Nullspace