Mapping/Linear algebra/Section
We discuss two classes of mappings which are in the framework of linear algebra very important. They are both so-called linear mappings.
It is a goal of linear algebra to determine, in dependence of the entries , whether the mapping defined by the matrix is injective, surjective or bijective, and how, in the bijective case, the inverse mapping looks like.
A healthy breakfast starts with a fruit salad. The following table shows how much vitamin C, calcium and magnesium various fruits have (in milligram with respect to 100 gram of the fruit).
apple | orange | grapes | banana | |
---|---|---|---|---|
vitamin C | ||||
calcium | ||||
magnesium |
This table yields a mapping, which assigns to a -tuple , representing the used fruits, the content of the resulting fruit salad with respect to vitamin C, calcium and magnesium in the form of a -tuplel . This mapping can be described with the matrix
using matrix multiplication as