The image of a function is the subset of a function's codomain which is the output of the function from a subset of its domain. (From Wikipedia)
In other words, while the codomain is the set of all possible values of the functions output, the image is specifically the subset of these that do appear, when the function is applied to all possible elements of the domain. This is sometimes referred to as the range.
keenan
Right—and when trying to solve any kind of equation (linear or otherwise) it is worth first asking if the target value is even in the image of the function (well-posedness). This question becomes especially tricky when solving equations involving functions (e.g., partial differential equations), and can be a fairly common source of error (and confusion!) in graphics algorithms.
The image of a function is the subset of a function's codomain which is the output of the function from a subset of its domain. (From Wikipedia)
In other words, while the codomain is the set of all possible values of the functions output, the image is specifically the subset of these that do appear, when the function is applied to all possible elements of the domain. This is sometimes referred to as the range.
Right—and when trying to solve any kind of equation (linear or otherwise) it is worth first asking if the target value is even in the image of the function (well-posedness). This question becomes especially tricky when solving equations involving functions (e.g., partial differential equations), and can be a fairly common source of error (and confusion!) in graphics algorithms.