Plan

• 2.1

2.1 Linear Transformation

• Recall a linear transformation is a map T such that T(x + y) = T(x) + T(y) and T(cx) = cT(x).

  • We can also apply this to a general linear combination.
  • Differentiate and integration are examples.
  • Reflections, projections (there are multiple versions)
  • Translation is not an example.
  • Identity and zero transformations

• null space and kernel, range and image

• Theorem: these are subspaces

• image of subspaces T(W)

• prove rank-nullity. Pick a basis for null space and extend.

• One-to-one