73. Transformation Scalar Multiplication

For a linear transformation and a scalar , define the scaled transformation pointwise:

The scaled transformation is itself linear.

73.1. Matrix correspondence

If has matrix , then has matrix :

So scaling a transformation = scaling its matrix entrywise.

73.2. Combined with sum: vector space of transformations

Together with sum, scalar multiplication makes the set of linear transformations into a vector space of dimension — isomorphic to the space of matrices.

73.3. Connections