DLA Terminology and notation

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Section 43.2 Terminology and notation

kernel (of a linear transformation $\funcdef{T}{V}{W}$ ): the collection of all vectors $\uvec{v}$ in the domain space $V$ for which $T(\uvec{v}) = \zerovec_W$
$\ker T$: notation for the kernel of a transformation $T$
nullity (of a linear transformation): the dimension of the kernel
image (of a linear transformation $\funcdef{T}{V}{W}$ ): the collection of all image vectors $T(\uvec{v})$ in the codomain space $W\text{,}$ as $\uvec{v}$ varies over all vectors in the domain space $V$
range (of a linear transformation $\funcdef{T}{V}{W}$ ): synonym for image
$\im T$: notation for the image of a transformation $T$
$R(T)$: alternative notation for the image of a transformation $T$
$T(V)$: alternative notation for the image of a transformation $\funcdef{T}{V}{W}$
rank (of a linear transformation): the dimension of the image