Rank and Nullity

Definition

Let

• $A$ : Matrix

Then

• $n=\dim [R(A)]=\dim [C(A)]$
• We call $n$ the rank of $A$
• We denote $n=\mathrm{rank}(A)$
• We call $\dim [N(A)]$ the nullity of $A$

¹

Theorem

Let $A$ : Matrix

Then $dim[R(A)]=dim[C(A)]$

Footnotes

1. Column space, Row space, Null space, Dimension ↩