null space

description

• null space of a linear transformation is the set of all vectors that are mapped to the zero vector by the transformation
• nontrivial null space is a null space that is not just the zero vector itself

calculation

• N(A) orthog to $R(A^T)$ , $x\in N(A),y\in R(A^T)$ → $x^{T}y=0$
• $N(A)=\{x\in R^n:Ax=0\}$