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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