Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 81

We discuss two binary operators on the set where V and W are vector spaces, namely the sum of two linear transformations and multiplication of a linear transformation by a scalar. Each operator produces a new linear transformation.

Definition 5.1 The sum of two linear transformations is a mapping from V to W and is defined by:

(5.1)

Definition 5.2 The scalar product of a linear transformation and a scalar is defined by:

(5.2)

Definition 5.3 Let , . Then the composition of and is defined by:

(5.3)

We check that the composition is a linear transformation as follows: