Linear Extension Theorem
  • Let:
    • 𝛽 =βŸ¨π‘1, 𝑏2, …,Β π‘π‘›βŸ©be the basis for vector space 𝑉
    • {𝑀1, 𝑀2, …, 𝑀𝑛} be arbitrary vectors in vector space π‘Š
  • then there exists a UNIQUE linear transformation 𝑇:π‘‰β†’π‘Š such that 𝑇(𝑣𝑖) = 𝑀𝑖 for all 𝑖

Proof