In this section, we consider a number of examples of linear transformations. Many of these transformations are studied in more detail in later sections. Recall that a function T with domain V and codomain W is denoted by . (See Appendix B.)
Let V and W be vector spaces over the same Geld F. We call a function a linear transformation from V to W if, for all and , we have
We often simply call T linear. The reader should verify the following properties ...