6-29.md

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title: 6/29

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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