Image.md (803B)
1 # Image 2 3 Khan U2 4 5 **Definition:** The image of a function is the total set of all outputs of a given function (transformation for vectors). 6 7 This is the same as [Range](Range.md) 8 9 Subsequently the preimage is the domain of the function with mappings to elements of the image. 10 11 ## Lin Alg Specific 12 13 The result of the tranformation of a subspace is the image of the subspace under T where T is the transformation. 14 15 Ex. 16 17 T(V) = image of V under T 18 19 We call this the image of T stated as im(T) when we are referring to any vector in R^n not necessarily a given subspace. The distinction here is that T(V) defines V as the codomain whereas im(T) defines the codomain as all possible vectors in R^n. 20 21 ## Set Notation 22 23 The image of the set S under f is defined as follows: 24 25 $img(S) = f(S) = \{f(s) | s \in S\}$