59. Domain
For a function , the domain is the set of inputs.
For a linear transformation , the domain is .
59.1. Domain vs codomain vs image
- Domain — where the inputs live ()
- Codomain — where outputs are allowed to live ()
- Image / Range — where outputs actually land (a subset of the codomain)
Example
from to :
- Domain:
- Codomain:
- Image: — only non-negative outputs
The image is a strict subset of the codomain (negatives like are in the codomain but not the image).
59.2. For matrices
If with an matrix, then:
- Domain = (number of columns of )
- Codomain = (number of rows of )
- Image = column space of ⊆
59.3. See also
- Codomain
- Image — what lands in the codomain
- Linear Transformation