Linear Transform

Suppose $(V,⊞,⊡)$ and $(W,\oplus ,\odot )$ are vector spaces. A linear transformation / map / function of $T:V\to W$ s.t $T(v⊞v)=T(u)\oplus T(v)$ $T(a⊡v)=a\odot T(v)$

Theorem

• Linear Transformations Preserve Additive Identities
• Linear Transformations Preserve Addition and Scaling

Applications

• Proving A Function Is Linear

Concepts

• Zero Transformation
• Identity Transformation