12.7 LINEAR TRANSFORMATION
Linear mappings from one vector space to another have acquired an important role in mathematics. Each linear transformation can be represented by a matrix, which enables us to work with the matrix in place of the transformation.
Definition 12.5 Let U and V be vector spaces over the same field F. A mapping T: U → V is said to be a linear transformation if
- T( + ) = T + T, ∀ , ∈ U
- T(α) = αT, ∀ α ∈ F, ∈ U
The conditions ...