Lattice

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0.1 Linear TransformationN96P

A linear transformation is a function $T:V\to W$ for vector fields $V,W$ such that

  1. $T(\mathbf{v}+\mathbf{w}) = T(\mathbf{v})+ T(\mathbf{w})$ for all $\mathbf{v},\mathbf{w}\in V$
  2. $T(\alpha\mathbf{v}) = \alpha T(\mathbf{v})$ for all $\mathbf{v}\in V$ and scalars $\alpha$