Definition:Kernel of Linear Transformation/Vector Space

Definition
Let $\struct {\mathbf V, +, \times}$ be a vector space.

Let $\struct {\mathbf V', +, \times}$ be a vector space whose zero vector is $\mathbf 0'$.

Let $T: \mathbf V \to \mathbf V'$ be a linear transformation.

Then the kernel of $T$ is defined as:


 * $\map \ker T := T^{-1} \sqbrk {\set {\mathbf 0'} } = \set {\mathbf x \in \mathbf V: \map T {\mathbf x} = \mathbf 0'}$

Also see

 * Definition:Null Space


 * Kernel of Linear Transformation contains Zero Vector