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